Sindbad~EG File Manager

/*  6.17.13,  problems read from simprev.mhw */
char *problems101[] = {
"1. (x^3yz^2)(xy^2z^3)",
"2. (2x^2)(3x^3)(5x^5)",
"3. (-x^3y^5)^7",
"4. (24x^3yz^4)/(6x^2y^3)",
"5. x^n(2x)^(2n)(3x)^(3n)",
"6. (x^2-1)(x^2 + 1) - (x^2-3)(x^2 + 3)",
"7. x^3 - (-x^2 + (x^2-6))",
"8. (2xy -(x+xy+y)) +(2y-(2x+xy+2y))",
"9. (x-2y)((3x+5y) - (5x+3y))(6x^2 + 7xy - 5y^2)",
"10. (1-3x)(x+1)-(x-3x^2)^2",
"11. (x - y)^2+17 (x - y) +16",
"12. (x-y)^2 - 6(x-y) + 9",
"13. (x+a)^3 + (x-a)^3",
"14. x^2+11x+18",
"15. 3x^2+24x+36",
"16. 10x^2 - 8x - 2",
"17. x^4 - 3x^2 - 4",
"18. (a+3)/(a^2-1) -4/(a-1)",
"19. ((2x) / (x+4) - 1/(x+4)) / (x+1-x/(x+4))",
"20. 3/(y^2+6y-16) - 1/(y-8) +1/(y+2)",
"21. (x+3) / (x^2+5x+6) - (5x - 1) / (x+2)",
"22. 3/(x^2+6x+9) - x/(x^2 - 9) +2/(x-3)",
"23. (1 / (x+2) - 3) / (4/x - x)",
"24. (1/x-1/y) / (1/x^2 - 1/y^2)",
"25. (x-1)/(x+4)-[(x-6)/(x^2+3x-4)]/[(x-4)/(x-1)]",
"26. (x/y+y/x+2) / ((y+1)/x+(y+1)/y)",
"27. (1/x+1/y+1/z) / (1/(xy)-1/(yz))",
"28. 3x^2y + x(xy+y(3y-x))",
"29. (x + 1/x - 2)(x^2 + x/(x-1))",
"30. x/(2-3/x) - x^2/(4x + 9/x -12)",
"31. [sqrt(x-4) + sqrt x]/ [sqrt(x-4) - sqrt x]",
"32. (x^2y)/(3xy^3)/(4x^4/(4x^2y^2))",
"33. ((x^2+3x - 4)/(x^2 - 3x - 4)) (x^2 - 5x+4)/(x^2+5x+4)",
"34. ((xy)^3 - 8) / (xy +2)",
"35. (3y - 4) / (y +2) + (3y) / (10+3y - y^2)",
"36. (2x) / (x+2) - 8x/(x^3+2x^2) - 3/x",
"37. 2/(x+1) - 3/(x+1)^2 + 1/(x^2 - 1)",
"38. (y^2 / x^2 - 1) / (y / x + 1)",
"39. (((x^2-xy)/(xy+y^2))/((x^2-y^2)/(x^2-2xy+y^2)))/((x^2-2xy+y^2) /(x^2y-xy^2))",
"40. root(3, 27x^5y^8)",
"41. (sqrt 2x)(sqrt (12xy^2) + sqrt (8x^2y))",
"42. (sqrt x - 2 sqrt y)( sqrt x + 2 sqrt y)",
"43. (sqrt(x) -2 sqrt(y))^2 +4 sqrt (xy)",
"44. ((sqrt x-1)^3 ) + x",
"45. (root(3, x) + root(3, y)) (root(3, x^2) - root(3, x) root(3, y) + root(3, y^2))",
"46. (sqrt x -1) (sqrt x^2 + sqrt x + 1)",
"47. (root(4, x))^2(sqrt y)  - (root(4, x)) ((root(4, x))(sqrt y) -(sqrt y) (2(sqrt y) -(root(4, x))))",
"48. ( sqrt x + 3) / (sqrt x - 3)",
"49. (3 sqrt y) / (x - 3 sqrt y)",
"50. (1 / ((sqrt x) - 2) - 1/2) / (sqrt x)",
"51. (1/(root(4, x))+1/(sqrt y)) / (1/(root(4, x))^2 - 1/(sqrt y)^2)",
"52. (3+1/((sqrt x) - (sqrt y))) / (1 - 3/((sqrt x)- (sqrt y)))",
""
};

/*  6.17.13,  problems read from algident.mhw */
char *problems102[] = {
"1. (x^2 + y^2)(x- y)(x+y) + y^4 = x^4",
"2. (x^2x^2 + x^4)x^4 + x^8= 3x^8",
"3. (x-1)(x-2)+(x-3)(x-4)= 2(x^2-5x+7)",
"4. (x^2-1)(x^2 + 1) + (x^2-3)(x^2 + 3)= 2(x^4-5)",
"5. (6x+4) - (4x-2) + (-x^2 -1)= -x^2 +2x+5",
"6. (x^2x^2 + x^4)x^4 - x^8 = x^8",
"7. (x-1)(x+1)+(x+1)(x-1)= 2(x^2-1)",
"8. (2x(a+bx^2)-2bx^3)(a+bx^2)^2 = 2ax(bx^2 +a)^2",
"9. ((a^2-x^2) + x^2)(a^2-x^2)= a^2(a-x)(a+x)",
"10. 2a - 3a(1-(b+c)/(b-c))= 2a(b+2c)/(b-c)",
"11. (a - 1/a)(1-1/(a+1)) = a-1",
"12. (a-4/a)/(a+4/a + 4) = (a-2)/(a+2)",
"13. [(x-1)/(x+1) - (x+1)/(x-1)]/ [(x-1)/(x+1) + (x+1)/(x-1)] = -2x/(x^2+1)",
"14. ((a-3b)/(3a-b) -1)(5 - (2a+6b)/(a+b))= -2",
"15. (a+b)/((a-c)(b-c)) - (b+c)/((a-b)(a-c)) - (a+c)/((a-b)(b-c)) = -2(b+c)/((a-b)(a-c))",
"16. (a/b - 9b/a)/((a+3b)^2/(3ab) - 4)= 3(a+3b)/(a-3b)",
"17. ((a-x -(a+x)(-1))/(a-x)^2)/((a+x)/(a-x))= 2a/((a-x)(a+x))",
"18. (1/16 - 1/x^2) / (x+4)= (x-4)/(16x^2)",
"19. (1 - 1/x^2) / ((x - 1)/x)= (x+1)/x",
"20. [x-2/(x+1)]/[x+(x-3)/(x+1)]= (x+2)/(x+3)",
"21. (1/x+1/y) / (1 / (x+y))= (x+y)^2/(xy)",
"22. (1/x+1/y) / (1/(xy))= x+y",
"23. (x-1)/(x+4)+[(x-6)/(x^2+3x-4)]/[(x-4)/(x-1)]= (x^2-4x-2)/(x^2-16)",
"24. (1/(x-y) - 3/(x+y))/(3/(x+y) + 1/(x^2-y^2))= 2(2y-x)/(3x-3y+1)",
"25. (x+2 - 3/(x+4)) / (x / (x+4)+1/(x+4))= x+5",
"26. (5/x+8/(2x+1)) / (6 /(2x+1) - 3/x)= -(18x+5)/3",
"27. (x/(x+1) +1) ((1-x^2)/(4x^2 -1))= (1-x)/(2x-1)",
"28. (1/(1-y) -y)/((y^2 -y+1)/(y^2 -2y+1)) = 1-y",
"29. (ab+b^2)/3 (3a/b^3) + (a+b)/b = ((a+b)/b)^2",
"30. (x-y)/(4y) ((8y^2)/(x^2 -xy)) - 3/x^2 = (2xy-3)/x^2",
"31. 1+ 24/(x-2)^2 ((4x-x^2-4)/(3(x+6))) =(x-2)/(x+6)",
"32. (4a/(2-a))/(2+ (a^2 +4)/(a-2))= -4/(a+2)",
"33. (2x^2 +10xy)/(x^2-25y^2)= (2x^2 -10xy)/(x^2 -10xy+25y^2)",
"34. (a^2 -4a +4)/(a^2 +ab-2a -2b) = (a^2-ab+2b-4)/(a^2 +2a +2b -b^2)",
"35. ((2x-3y)^2 +2x -3y)/(4x^2 -9y^2 +2x+3y) = (4x^2 -12xy+9y^2)/(4x^2 -9y^2)",
"36. (x -(x^2+y^2)/(x+y)) (1/y +2/(x-y)) =1",
"37. (2x+1-1/(1-2x))/(2x-4x^2/(2x-1))= -2x",
"38. (p-q +(4q^2 -p^2)/(p+q))/(pq/(p^2-q^2) +q/(q-p))= 3(q-p)",
"39. ((6a+1)/(a^2-6a) + (6a-1)/(a^2 +6a)) ((a^2-36)/(a^2+1))= 12/a",
"40. ((5x+y)/(x^2-5xy) + (5x-y)/(x^2 +5xy))( (x^2 -25y^2)/(x^2+y^2))= 10/x",
"41. (a+b -2ab/(a+b))/( b/a+ (a-b)/(a+b))= a",
"42. (4xy/(y^2-x^2))/(1/(y^2-x^2) +1/(x^2+2xy+y^2))= 2x(x+y)",
"43. (x/y +1)^2 + (x/y-1)^2 = 2(x^2+y^2)/y^2",
"44. (p/q+q/p)^2 - (p/q- q/p)^2 = 4",
"45. (((x+y)/(xy))^2) / (1/x^2 +1/y^2 + (2/(x+y))(1/x+1/y))=1",
"46. ( (1-a)(1-b)/(1+ab) -1)^2 + (1-a^2)(1-b^2)/(1+ab)^2=1",
"47. ((1/(x-y)^2 +2/(x^2-y^2) +1/(x+y)^2) (x^2-y^2)^2 ) / ((x+y)^2 +2(x^2-y^2) +(x-y)^2)=1",
""
};

/*  6.17.13,  problems read from trigeval.mhw */
char *problems103[] = {
"1. sin (deg (0))",
"2. cos (deg (0))",
"3. tan (deg (0))",
"4. cot (deg (30))",
"5. cot (-deg (30))",
"6. sec (deg (30))",
"7. sec (-deg (30))",
"8. csc (deg (30))",
"9. csc (-deg (30))",
"10. sin (deg (45))",
"11. sin (-deg (45))",
"12. cos (deg (45))",
"13. cos (-deg (45))",
"14. tan (deg (45))",
"15. tan (-deg (45))",
"16. cot (deg (60))",
"17. cot (-deg (60))",
"18. sec (deg (60))",
"19. sec (-deg (60))",
"20. csc (deg (60))",
"22. csc (-deg (60))",
"23. sin (deg (90))",
"24. cos (deg (90))",
"25. cot (deg (120))",
"26. sec (deg (120))",
"27. csc (-deg (120))",
"28. sin (deg (150))",
"29. cos (-deg (150))",
"30. tan (deg (150))",
"31. sin (deg (180))",
"32. cos (deg (180))",
"33. tan (deg (180))",
"34. cot (-deg (210))",
"35. sec (deg (210))",
"36. csc (deg (210))",
"37. sin (deg (240))",
"38. cos (-deg (240))",
"39. tan (deg (240))",
"40. cot (deg (270))",
"41. sec (-deg (270))",
"43. sin (deg (300))",
"44. cos (deg (300))",
"45. tan (deg (300))",
"46. cot (deg (330))",
"47. sec (deg (330))",
"48. csc (-deg (330))",
"49. sin(pi/6)",
"50. cos(pi/6)",
"51. tan(-pi/6)",
"52. sec(pi/4)",
"53. csc(pi/4)",
"54. cot(pi/4)",
"55. sin(pi/3)",
"56. cos(-pi/3)",
"57. tan(pi/3)",
"58. csc(pi/2)",
"59. cot(pi/2)",
"60. sin(2pi/3)",
"61. cos(2pi/3)",
"62. tan(-2pi/3)",
"64. sec(5pi/6)",
"65. csc(5pi/6)",
"66. cot(-5pi/6)",
"67. sin(pi)",
"68. cos(pi)",
"69. tan(pi)",
"70. sec(3pi/2)",
"71. csc(3pi/2)",
"72. cot(3pi/2)",
"73. sin(-11pi/6)",
"74. cos(11pi/6)",
"75. tan(11pi/6)",
"76. sec(5pi/3)",
"77. csc(5pi/3)",
"78. cot(5pi/3)",
"79. sin(5pi/4)",
"80. cos(-5pi/4)",
"81. tan(5pi/4)",
"82. sec (7pi/6)",
"83. csc(7pi/6)",
"84. cot(7pi/6)",
"85. sin(5pi/6)",
"86. cos(5pi/6)",
"87. tan(5pi/6)",
"88. sec(3pi/4)",
"89. csc(3pi/4)",
"90. cot(-3pi/4)",
""
};

/*  6.17.13,  problems read from basident.mhw */
char *problems104[] = {
"1. (sin (-x)) / cos (-x) = - tan x",
"2. sec (-x) = sec x",
"3. cot u sec u sin u = 1",
"4. sqrt (tan^(2) x +1) = abs(sec x)",
"5. (sin^2 x + cos^2 x)^5 = 1",
"6. 1 / ((sec^3 x ) cos^4 x) = sec x",
"7. (sin x) (csc x - sin x) = cos^2 x",
"8. (1 / csc^2 x) + (1/ sec^2 x) = 1",
"9. (1 / sec^2 t) = 1 - (1 / csc^2 t)",
"10. (sin x + cos x)^2 + (sin x - cos x)^2 = 2",
"11. (1+cos x)(1 - cos x) = sin^2 x",
"12. (sin x +cos x)^2 = 1+2(sin x) cos x",
"13. (1+tan^2 x) / tan^2 x = csc^2 x",
"14. tan x+1 = (sec x)(sin x+cos x)",
"15. (cos x) / (1 - sin^2 x) = sec x",
"16. (sin x) / csc x + (cos x) / sec x = 1",
"17. (1+sec x) / csc x = sin x + tan x",
"18. sin^4 x + cos^4 x = 1 - 2 (sin^2 x) cos^2 x",
"19. sin^2 t + tan^2 t + cos^2 t = sec^2 t",
"20. cos^4 x + 2(cos^2 x) sin^2 x + sin^4 x = 1",
"21. (cos^2 t)/sin t + sin t = csc t",
"22. cot^2 x sin^2 x = 1-sin^2 x",
"23. (1- cos^2 y)/((1-sin y)(1+sin y)) = tan^2 y",
"24. ((cot u) cos u) / (csc^2 u - 1) = sin u",
"25. (sin x + tan x) / (1 + sec x) = sin x",
"26. sin x = ((tan x) cot x) / csc x",
"27. (tan x) (tan x + cot x) = sec^2 x",
"28. (1 + sin x) / cos x = (cos x) / (1 - sin x)",
"29. (tan^2 x) cos^2 x = 1 - cos^2 x",
"30. 1 / (csc x - sin x) = (sec x) tan x",
"31. (cos x)/(csc x + 1) + (cos x)/(csc x-1) = 2 tan x",
"32. (csc^4 x-1)/cot^2 x = 2 + cot^2 x",
"33. ((1 - cos x) / sin x) + (sin x) / (1 - cos x) = 2 csc x",
"34. sec x - cos x = (1 - cos^2 x) / cos x",
"35. (csc x) / (tan x + cot x) = cos x",
"36. (1+csc x) / (cot x + cos x) = sec x",
"37. (2 cos^2 x) - 1 = 1 - 2 sin^2 x",
"38. (2 sin^2 x - 1) / (sin x+cos x) = sin x - cos x",
"39. (tan x - 1)^2 = sec^2 x - 2 tan x",
"40. cos x + (cos x) tan^2 x = sec x",
"41. (sin x) (1+cos x) = (sin^3 x) / (1 - cos x)",
"42. (sin u)/(1-cos^2 u) = csc u",
"43. cot x + sec x = (cos x + tan x)/sin x",
"44. ((cot x) / (1 - tan x)) + (tan x) / (1 - cot x) = 1+(sec x) csc x",
"45. (tan x - tan y) / (cot x - cot y) = -(tan x)tan y",
"46. (tan x) / (sec x - 1) = (sec x + 1) / tan x",
"47. (tan x - 1) / (tan x +1) = (1 - cot x) / (1 + cot x)",
"48. sec^2 u + csc^2 u = sec^2 u csc^2 u",
"49. (3 cos^2 z + 5 sin z - 5)/cos^2 z = (3sin z-2)/(1+sin z)",
"50. (1-csc y)/(1+csc y) = (sin y -1)/(sin y + 1)",
"51. (cos^3 u + sin ^3 u)/(cos u + sin u) = 1 - sin u cos u",
"52. tan^2 x - sin^2 x = (tan^2 x) sin^2 x",
"53. sin^4 x - cos^4 x = sin^2 x - cos^2 x",
"54. 1 - 2 cos^2 x + cos^4 x = sin^4 x",
"55. sec^4 x - tan^4 x = 1 + 2 tan^2 x",
"56. sec^2 x + csc^2x = (sec^2 x) csc^2 x",
"57. sin^4 x - 2 sin^2 x + 1 = cos^4 x",
"58. sin^4 x + cos^2 x = sin^2 x+cos^4 x",
"59. (sin x)/(1-cos x) = (1+cos x)/sin x",
""
};

/*  6.17.13,  problems read from addform.mhw */
char *problems105[] = {
"1. sin(x + 2 pi) = sin x",
"2. cos(x + 2 pi) = cos x",
"3. tan(x + pi) = tan x",
"4. cot(x + pi) = cot x",
"5. cos(x+2 m pi) = cos x",
"6. sin(x + 2 m pi) = sin x",
"7. cot (x + m pi) = cot x",
"8. tan( x+ m pi) = tan x",
"9. tan(x + pi/2) = -cot x",
"10. cos (pi/2 + x) = - sin x",
"11. (sin (x+pi/2)) / cos (x+pi/2) = - cot x",
"12. cot (pi/2+x) = - tan x",
"13. sec (pi/2+ x) = - csc x",
"14. cos (x - pi) = - cos x",
"15. sin (pi+x) = - sin x",
"16. cos (x+pi) = - cos x",
"17. cos (pi - x) = - cos x",
"18. tan (pi - x) = - tan x",
"19. sin (x - pi) = - sin x",
"20. csc (pi - x) = csc x",
"21. cos (3 pi/2 - x) = - sin x",
"22. sin (3 pi/2 - x) = - cos x",
"23. tan (3 pi/2 - x) = cot x",
"24. cos ( x - pi/4) = (sqrt 2) /2 (cos x + sin x)",
"25. tan ( pi/4 + x) = (1+tan x) / (1 - tan x)",
"26. sin (pi/4+x) - sin (pi/4 - x) = sqrt 2 sin x",
"27. tan (x + pi/4) = (1+tan x) / (1 - tan x)",
"28. sin x + cos x = sqrt 2 sin (x + pi/4)",
"29. cos (pi/6 + x) + sin (x - pi/3) = 0",
"30. tan ( x - 3 pi/4) = (1 + tan x) / (1 - tan x)",
"31. sin (pi/6 - x) = 1/2 (cos x - (sqrt 3) sin x)",
"32. sin (x + y) sin (x - y) = sin^2 x - sin^2 y",
"33. sin (x+y) + sin(x - y) = 2 sin x cos y",
"34. cos (x+y) cos (x - y) = cos^2 x - sin^2 y",
"35. sin(x+y) - sin (x - y) = 2 cos x sin y",
"36. cos x cos ( x - y) + sin x sin (x - y) = cos y",
"37. (sin (x+y)) / sin (x - y) = (cot y + cot x) / (cot y - cot x)",
"38. (sin (x+y)) / sin (x - y) = (tan x + tan y) / (tan x - tan y)",
"39. cos (x+y) - cos (x - y) = - 2 sin x sin y",
"40. (cos (x+y)) / cos (x - y) = ( cot x - tan y) / (cot x + tan y)",
"41. (cos ( x - y)) / (sin x cos y) = cot x + tan y",
"42. sin (x+y) sec (x+y) = (tan x+tan y) / (1 - tan x tan y)",
"43. csc (x+y) = (csc x csc y) / (cot x + cot y)",
"44. (sin(x+h) - sin x)/h = (sin x)((cos h -1)/h) + (cos x) ((sin h)/h)",
"45. (cos(x+h)-cos x)/h = (cos x)((cos h -1)/h) - (sin x)((sin h)/h)",
"46. tan x + cot y = cos(x-y)/(cos x sin y)",
"47. tan(x+y) = (cot x + cot y)/(cot x cot y -1)",
"48. tan(x-y) = (cot y - cot x)/(cot x cot y +1)",
"49. sin (pi/6 + x) = 1/2 (cos x + (sqrt 3) sin x)",
"50. cos (pi/6 + x) cos (pi/6 - x) - sin (pi/6 + x) sin (pi/6 - x) = 1/2",
""
};

/*  6.17.13,  problems read from doubangl.mhw */
char *problems106[] = {
"1. (sin x + cos x)^2 = 1 + sin 2x",
"2. (sin x - cos x)^2 = 1 - sin 2x",
"3. sin^2 x = (1/2) (1- cos 2x)",
"4. sin 2x = (2 tan x) / sec^2 x",
"5. sin 2x = (2 tan x) / (1+tan^2 x)",
"6. (2+sin 2x) / 2 = (sin^3 x - cos^3 x) / (sin x - cos x)",
"7. 2 (tan x - cot x) / (tan^2 x - cot^2 x) = sin 2x",
"8. 2 cot(2 theta) = cot theta - tan theta",
"9. 1- cos 2x = tan x sin 2x",
"10. cos 4 theta = 2 cos^2 2 theta - 1",
"11. (sin 2x) / (1+cos 2x) = tan x",
"12. cos^2 x = 1/2 (cos 2x+1)",
"13. cos 2x = (1 - tan^2 x) / (1+tan^2 x)",
"14. 2 cos^2 t = (cot t) sin 2t",
"15. (1+sin 2x+cos 2x) / (1 + sin 2x - cos 2x) = cot x",
"16. cos 2x = cos^4 x - sin^4 x",
"17. (tan x) sin 2x = 1 - cos 2x",
"18. (1 + 2 cos x)^2 = 3 + 4 cos x + 2 cos 2x",
"19. sin^4 x + cos^4 x = (1 + cos^2(2x)) / 2",
"20. (sin^2 x) cos^2 x = 1/8 (1 - cos 4x)",
"21. cos 4u = 1 - 8 (sin^2 u) cos^2 u",
"22. cos 4x = 8 cos^4 x - 8 cos^2 x + 1",
"23. sin 4x = 4 (sin x) cos^3 x - 4 (sin^3 x) cos x",
"24. 2 sin^2 (2x) + cos 4x = 1",
"25. sin 4x = (cos x) (4 sin x - 8 sin^3 x)",
"26. (1 - cos 4x) (2 + tan^2 x + cot^2 x) = 8",
"27. sin^4 x = 1/8 (3 - 4 cos 2x + cos 4x)",
"28. cos^4 x = 1/8 (3+4cos 2x + cos 4x)",
"29. tan 2x = (2 tan x)/(1- tan^2 x)",
"30. cot theta + tan theta = 2 csc(2 theta)",
"31. 4 (sin^6 x + cos^6 x) = 4 - 3 sin^2 (2x)",
"32. cot 2x = (cot x - tan x) / 2",
"33. cot 2x = (csc x - 2 sin x ) / (2 cos x)",
"34. tan 2x = (2 cot x) / ( cot^2 x - 1)",
"35. 1/2 tan 2x = 1 / ( cot x - tan x)",
"36. tan 2x = (2 cos x) / (csc x - 2 sin x)",
"37. (sin t + cos t)(sin^3 t + cos^3 t)/(1+ sin 2t) = 1 - (1/2) sin 2t",
"38. 2 csc 2x = (1+tan^2 x)/tan x",
"39. 2 csc 2x = tan x + cot x",
"40. csc 2x = 1/2 (csc x) sec x",
"41. sec^2 x = (sec 2x) (2- sec^2 x)",
"42. tan x = csc 2x - cot 2x",
"43. ((csc^2 x) sec^2 x) / (cot^2 x - tan^2 x) = sec 2x",
"44. (1 - cos 8x) / 8 = sin^2 (2x) cos^2 (2x)",
"45. tan(2 theta) + sec(2 theta) = (1+ tan theta)/(1- tan theta)",
"46. sin 8x = 2 (sin 4x) cos 4x",
"47. cos 6x = 32 cos^6 x - 48 cos^4 x + 18 cos^2 x - 1",
"48. sin(6 theta) = 2(sin theta cos theta)(16 cos^4 theta - 16 cos^2 theta + 3)",
"49. cos(6 theta) = 32 cos^6 theta - 48 cos^4 theta + 18 cos^2 theta - 1",
"50. (cot^2 theta + 1)/(cot^2 theta-1) = sec 2 theta",
"51. (sin 3t)/cos t + (cos 3t)/sin t = 2 cot(2t)",
"52. cos 8x = cos^2 4x - sin^2 4x",
"53. cos 2x = cos^4 x - sin^4 x",
"54. (1 - cos 2x) / tan x = sin 2x",
"55. sin 3x = 3 sin x cos^2 x -  sin^3 x",
"56. csc 2x - cot 2x = tan x",
"57. (1 - cos 2x) / sin 2x = tan x",
"58. cot x - tan x = (4 cos^2 x - 2) / sin 2x",
"59. ((1 - cot x) / csc x)^2 = 1 - sin 2x",
"60. (cos 2x - cos 4x) / (2 sin 3x) = sin x",
"61. tan^2 x - cot^2 x = - 4 cot 2x csc 2x",
"62. 1 - 4 sin^4 x = 2 cos 2x - cos^2 2x",
""
};

/*  6.17.13,  problems read from halfangl.mhw */
char *problems107[] = {
"1. 2 sin(x/2) cos(x/2) = sin x",
"2. sin x = (2 tan (x/2))/(1+ tan^2(x/2))",
"3. sin x = (2 tan (x/2)) / sec^2 (x/2)",
"4. cos x = 1 - 2sin^2 (x/2)",
"5. cos^2(x/2) - sin^2 (x/2) = cos x",
"6. cos x cot (x/2) sec^2 (x/2) = 2 cot x",
"7. tan(pi/4 + theta/2) = sec theta + tan theta",
"8. cos x = (1 - tan^2(x/2))/(1 + tan^2(x/2))",
"9. cos^2 (x/2) = 1/2 (cos x +1)",
"10. (cos (x/2) - sin (x/2))^2 = 1 - sin x",
"11. 2 cos^2(x/2) = (sin^2 x)/(1-cos x)",
"12. cot(pi/4 + theta/2) + tan theta = sec theta",
"13. 2 sin^2 (x/2) + cos x = 1",
"14. 2 sin^2(x/2) = (sin^2 x)/(1+cos x)",
"15. sin^2(x/2) =(sec x - 1)/(2 sec x)",
"16. sin^2(x/2) =(tan x - sin x)/(2 tan x)",
"17. 2 cos^2 (x/2)  = cot(x/2)   sin x",
"18. cos x = cos^4 (x/2)  - sin^4 (x/2)",
"19. 1 - 4sin^4 (x/2) = 2 cos x - cos^2 x",
"20. sin^4 (x/2)  + cos^4 (x/2)  = (1 + cos^2 x) / 2",
"21. cos 2x = 8 cos^4 (x/2)  - 8 cos^2 (x/2)  + 1",
"22. tan (x/2)  = csc x - cot x",
"23. tan(x/2) = (1-cos x)/sin x",
"24. tan(x/2)  - sin x = - (sin x)/ (1 + sec x)",
"25. tan(x/2) = (sin 2x - sin x)/(cos 2x + cos x)",
"26. tan x = (2 tan (x/2))/(1- tan^2 (x/2))",
"27. tan^2(x/2)= (sec x - 1)/ (sec x + 1)",
"28. tan^2(x/2)= 2/(1 + cos x) - 1",
"29. tan^2(x/2) -2 csc x tan(x/2) +1 = 0",
"30. cos^4 (x/2) - sin^4 (x/2) = cos x",
"31. 4 (sin^6 (x/2)  + cos^6 (x/2)) = 4 - 3 sin^2 x",
"32. cot x = (cot (x/2) - tan (x/2)) / 2",
"33. cot x = (cot^2(x/2) - 1)/(2 cot(x/2))",
"34. cot (x/2) = csc x + cot x",
"35. 1/2 tan x = 1 / (cot (x/2)-tan (x/2))",
"36. 2 csc x = (1+tan^2 (x/2))/tan (x/2)",
"37. 2 csc x = csc (x/2) sec (x/2)",
"38. sec^2 (x/2)  = (sec x) (2- sec^2 (x/2))",
"39. (tan (x/2) + cot (x/2))/( cot (x/2) - tan (x/2)) = sec x",
"40. (1 + sin x)/ sin x = 1 + 1/2 sec (x/2) csc (x/2)",
"41. cos 3x = 32 cos^6 (x/2)  - 48 cos^4 (x/2)  + 18 cos^2 (x/2)  - 1",
"42. tan(3pi/4 - theta/2) + tan theta + sec theta = 0",
"43. (sin 2 theta + 2 sin theta)/(sin 2 theta - 2 sin theta) + cot^2(theta/2) = 0",
"44. sin^4(theta/2) - 6 sin^2(theta/2) cos^2(theta/2) + cos^4(theta/2) = cos(2 theta)",
"45. cos^2 (x/2) = (tan x + sin x) / (2 tan x)",
"46. (tan x - sin x) / (2 tan x) = sin^2 (x/2)",
"47. sec x = sec^2 (x/2)/(2 - sec^2 (x/2))",
"48. cos (2x) = 8 cos^4 (x/2) - 8 cos^2 (x/2) + 1",
"49. (sec x - 1)/(sin x sec x) = tan (x/2)",
""
};

/*  6.17.13,  problems read from prodiden.mhw */
char *problems108[] = {
"1. sin 4x sin 5x",
"2. sin theta sin 2 theta",
"3. sin theta sin 3 theta",
"4. sin theta sin 7 theta",
"5. sin (deg (15)) sin(deg (45))",
"6. sin (deg (105)) sin (deg (165))",
"7. 2 sin 5x sin x",
"8. sin 3x sin (-2x)",
"9. sin 2x sin 3y",
"10. sin 4x sin x",
"11. sin 5x sin x",
"12. sin (x+y) sin(x-y)",
"13. sin 2x sin 6x",
"14. cos (deg (15)) sin (deg (15))",
"15. sin theta cos 5 theta",
"16. sin theta cos 3 theta", 
"17. sin theta cos 2 theta",
"18. sin 4x cos 5x",
"19. 6 sin (pi/4) cos (pi/4)",
"20. 4 sin (pi/3) cos (5 pi/6)",
"21. sin x cos y",
"22. sin 3x cos x",
"23. sin 4x cos x",
"24. sin 5x cos x",
"25. 2 cos (9x/2) sin (5x/2)",
"26. sin (deg (45)) cos (deg (75))",
"27. cos (deg (75)) sin (deg (15))",
"28. 2 sin 9x cos 3x",
"29. sin (- 4x) cos 8x",
"30. cos 3x sin 9x",
"31. cos x cos y",
"32. cos x cos 2x",
"33. cos 4x cos 5x",
"34. cos 5x cos x",
"35. cos 4x cos 12x",
"36. cos 4x cos 14x",
"37. cos (- 4x) cos 6x",
"38. cos theta cos 2 theta",
"39. cos (x+y) cos (x-y)",
"40. 2 cos (10pi x) cos (pi x)",
"41. cos (deg (15)) cos (deg (17))",
"42. cos (deg (75)) cos (deg (45))",
"43. sin x cos y + cos x sin y",
"44. cos 7x sin x + cos x sin 7x",
"45. cos x cos (x/2) sin (3x/2)",
"46. 4 sin x cos (x/2) sin (3x/2)",
"47. sin 2x sin 4x sin 6x",
"48. cos x cos 2x cos 3x",
"49. csc x sec x",
// 50. tan (x+y) tan (x-y),
""
};

/*  6.17.13,  problems read from factiden.mhw */
char *problems109[] = {
"1. sin(deg(70))-sin (deg(110)) = 0",
"2. (cos x - cos 5x) ( cos x+cos 5x) = sin 4x sin 6x",
"3. 2 sin x cos (x+y) = sin (2x+y) - sin y",
"4. sin(pi/3 + theta) - sin(pi/3 - theta) = sin theta",
"5. sin(theta + pi/4) + cos(theta + pi/4) = sqrt 2 cos theta",
"6. (sin alpha + sin beta)/(cos alpha + cos beta) = tan((alpha + beta)/2)",
"7. (sin 2 theta + sin 4 theta)/(cos 2 theta - cos 4 theta) = cot theta",
"8. cos (pi/6+x) cos (pi/6 - x) - sin (pi/6+x) sin (pi/6 - x) = 1/2",
"9. sin(x+y)sin(x-y)= sin^2 x - sin^2 y",
"10. cos(x+y)cos(x-y)= cos^2 x - sin^2 y",
"11. sin(x+y)sin(x-y)= cos^2 y - cos^2 x",
"12. (sin(deg(140))-sin (deg(20))) / (cos(deg(140))+cos (deg(20))) = sqrt 3",
"13. (cos(deg(50))-cos (deg(10))) / (sin (deg(10))-sin (deg(50))) = (sqrt 3)/3",
"14. (cos 2x - cos 3x) / (sin 3x+sin 2x) = (sin x) / (1+cos x)",
"15. (sin 5x - sin 4x) / (cos 5x+cos 4x) = (1 - cos x) / sin x",
"16. tan ((x+y) / 2) tan ((x - y) / 2) = - (cos x - cos y) / ( cos x+cos y)",
"17. cot ((x+y) / 2) cot ((x - y) / 2) = - (cos x+cos y) / (cos x - cos y)",
"18. (sin 4x - sin 2x) / (cos 4x + cos 2x) = tan x",
"19. (cos 2x - cos 6x) / (sin 6x - sin 2x) = tan 4x",
"20. (cos 3x+cos x) / (sin 3x+sin x) = cot 2x",
"21. (cos x-cos 5x) / (sin x cos x) = 4sin 3x",
"22. (sin 6y+sin 4y) / (sin y sin 5y) = 2 cot y",
"23. (cos 5x - cos 7x) / (sin 7x - sin 5x) = tan 6x",
"24. (cos 5x+cos 2x) / (sin 5x+sin 2x) = cot (7x / 2)",
"25. (sin x+sin y) / (cos x - cos y) = - cot ((x - y) / 2)",
"26. (sin 3x+sin 7x) / (cos 3x-cos 7x) = cot 2x",
"27. (cos x-cos y) / (sin x+sin y) = - tan ((x-y)/2)",
"28. (sin x - sin y) / (cos x - cos y) = - cot ((x+y) / 2)",
"29. (cos x+cos 9x) / (sin x+sin 9x) = cot 5x",
"30. (sin 3x+cos 3x) / (cos x- sin x) = 1 + 2 sin 2x",
"31. (sin 2x+sin 2y) / (cos 2x+cos 2y) = tan (x+y)",
"32. (sin 5x+sin 3x) / (sin 5x - sin 3x) = tan (4x) / tan x",
"33. (sin x+sin 2x+sin 3x) / (cos x+cos 2x+cos 3x) = tan 2x",
"34. (sin 2x - sin 3x+sin 4x) / (cos 2x - cos 3x+cos 4x) = tan 3x",
"35. (sin x+sin 3x+sin 5x) / (cos x+cos 3x+cos 5x) = tan 3x",
"36. (cos x+cos 4x+cos 7x) / (sin x+sin 4x+sin 7x) = cot 4x",
"37. (cos 8x + cos 4x) / (cos 8x - cos 4x) = - cot 6x cot 2x",
"38. cos(2 theta - pi/4) - cos(2 theta + pi/4) = sqrt 2 sin 2 theta",
"39. (sin x - sin y) / (sin x+sin y) = tan ((x - y)/2) / tan ((x+y)/2)",
"40. cot x = (sin(x+y)-sin(x-y))/(cos(x-y) - cos(x+y))",
"41. sin x + sin 2x + sin 3x = (1+2cos x) sin 2x",
"42. cos y + cos 2y + cos 3y = (1+ 2cos y) cos 2y",
"43. (sin u - sin 7u) / (2sin^2 (2u) -1) =  2 sin 3u",
"44. (sin u - sin 3u) / (sin^2 u -cos^2 u) =  2 sin u",
"45. (sin 2x)/sin x - (cos 2x)/cos x = sec x",
"46. (2 sin 2x)/(sin 3x + sin x) = sec x",
"47. (cos v+cos u) / (sin v + sin u) = cot ((u+v)/2)",
""
};

/*  6.17.13,  problems read from simptrig.mhw */
char *problems110[] = {
"1. (sin theta cot theta  + cos^2 theta)/(1+cos theta)",
"2. (csc^2 theta - cot^2 theta)/sec^2 theta",
"3. 1 - 8 (sin^2 theta) cos^2 theta",
"4. (sec theta tan theta - sin theta)/sin^3 theta",
"5. cos^2 theta - cos 2 theta",
"6. 1/(sin theta cos theta) - (cos theta)/sin theta",
"7. (csc theta cot theta - cos theta)/cos theta",
"8. (csc theta - cot theta)/(sec theta -1)",
"9. 2 (tan theta - cot theta) / (tan^2 theta - cot^2 theta)",
"10. 3/(1-cos theta) - 3/(1+cos theta)",
"11. (1- sin^2 theta) (1+ tan^2 theta)",
"12. (1+sin 2theta+cos 2theta) / (1 + sin 2theta - cos 2theta)",
"13. (csc theta -1)(sin theta + 1)",
"14. (sin theta + cos theta)^2 - sin 2theta",
"15. (sin 2theta)/(2sin theta)",
"16. (tan theta + 1)(sin theta - cos theta) + cos theta",
"17. 2 (sin theta)/(sec theta -1) + 2 (sin theta)/(sec theta + 1)",
"18. cos^3 theta + sin^2 theta cos theta",
"19. (tan theta)/sec (-theta)",
"20. 1 + (cot theta + csc theta)^2 - 2 (cos theta)/sin^2 theta",
"21. (cos^4 theta + 1 - sin^4 theta) sec^2 theta",
"22. (csc theta) (csc theta + sin (-theta))",
"23. 4 (sin^6 theta + cos^6 theta)",
"24. (sin^3 theta - cos^3 theta)/ (1 + sin theta cos theta) + cos theta",
"25. (tan theta + cot theta)^2 cos^2 theta - 1",
"26. (sin 2theta - sin 3theta+sin 4theta) / (cos 2theta - cos 3theta+cos 4theta)",
"27. ((csc^2 theta) sec^2 theta) / (cot^2 theta - tan^2 theta)",
"28. (sec theta - tan theta)^2 (1+ sin theta)^2 + sin^2 theta",
"29. ((csc theta + cot theta)^2 + 1)/ (sec theta csc theta + sec theta cot theta)",
"30. 2sin theta tan theta + tan theta - 2sin theta - 1",
"31. (sec theta - cos theta)/ tan theta",
"32. (2 + sec^2 theta) tan^4 theta + 3 sec^2 theta - 2",
"33. 1 - 3 sin^2 theta cos^2 theta - sin^6 theta",
"34. 1/(1-sin theta) + 1/(1 + sin theta)",
"35. tan theta cos theta csc theta",
"36. csc theta cot theta - cos theta - cos theta cot theta",
"37. tan 2 theta + 3 cot 2 theta",
"38. cos theta tan theta + sin^2 theta - 1 + sin theta",
"39. csc theta cos^2 theta + sin theta",
"40. (cot theta + 1)(cos theta - sin theta) + sin theta",
"41. (1-cos theta)(csc theta + cot theta)",
"42. cos theta + sin theta tan theta",
"43. tan^2 theta - sin^2 theta",
"44. sqrt((csc theta + 1)/(csc theta - 1)) + sqrt((csc theta - 1)/(csc theta + 1))",
"45. 2sin theta cos^3 theta + 2sin^3 theta cos theta",
"46. (cos theta sec theta)/tan theta",
"47. 4 sin^2 theta sec^2 theta - 4 cos^2 theta tan^2 theta - cos^4 theta - 2 sin^2 theta +1",
"48. ((sqrt sin^2 theta)/ sqrt(1+cos theta) + sqrt(tan^2 theta cos^2 theta)/ sqrt(1-cos theta)) (sqrt(1-cos theta) - sqrt(1+cos theta))",
"49. sec^4 theta- 2sec^2 theta tan^2 theta + tan^4 theta",
"50. (tan 2theta)/(tan 4theta - tan 2theta)",
""
};

/*  6.17.13,  problems read from trigiden.mhw */
char *problems111[] = {
"1. sin^2 x cot^2 x + cos^2 x tan^2 x = 1",
"2. (sin x + cos x)^2 - (sin x - cos x)^2 = 4 sin x cos x",
"3. 1 - 2 cos^2 x + cos^4 x = sin^4 x",
"4. (sin theta cot theta  + cos^2 theta)/(1+cos theta) = cos theta",
"5. (sec theta tan theta - sin theta)/sin^3 theta = sec^2 theta",
"6. (csc theta cot theta - cos theta)/cos theta = cot^2 theta",
"7. ((1+sin x) / (1+cos x)) ((1+sec x) / (1+csc x)) = tan x",
"8. 3/(1-cos theta) - 3/(1+cos theta) = 6 cot theta csc theta",
"9. (1 - cos x) / sin x = (sin x) / (1+cos x)",
"10. (csc theta -1)(sin theta + 1) = cos theta cot theta",
"11. (tan theta + 1)(sin theta - cos theta) + cos theta = sin theta tan theta",
"12. 1- (sin^2 x) / (1 + cos x) = cos x",
"13. (1 - tan x) (1 - cot x) = 2 - sec x csc x",
"14. 2 (sin theta)/(sec theta -1) + 2 (sin theta)/(sec theta + 1) = 4 cot theta",
"15. (sec theta - tan theta)^2 (1+ sin theta)^2 + sin^2 theta = 1",
"16. (cos^4 theta + 1 - sin^4 theta) sec^2 theta = 2",
"17. 1 + (cot theta + csc theta)^2 - 2 (cos theta)/sin^2 theta = 2 csc^2 theta",
"18. (sin^3 theta - cos^3 theta)/(1+sin theta cos theta)+cos theta = sin theta",
"19. 1 - 3 sin^2 theta cos^2 theta - sin^6 theta = cos^6 theta",
"20. (tan theta + cot theta)^2 cos^2 theta - 1 = cot^2 theta",
"21. 1/ (1+sin x) + 1/ (1 - sin x) = 2 sec^2 x",
"22. ((csc theta + cot theta)^2 + 1)/ (sec theta csc theta + sec theta cot theta) = 2 cot theta",
"23. (cot x) (cot x + csc x) = (cos x) / (1 - cos x)",
"24. (2 + sec^2 theta) tan^4 theta + 3 sec^2 theta - 2 = sec^6 theta",
"25. (sec theta)/(1- tan theta) + (csc theta)/(1+tan theta) = (csc theta)/(1- 2 sin^2 theta)",
"26. (cot^2 x) / (1 - sin x) = csc^2 x + csc x",
"27. (sin^2 theta sec^2 theta - cos^2 theta tan^2 theta)/(2 sin^2 theta - 1 + cos^4 theta) = sec^2 theta",
"28. sin x + cos x = (sin x) / (1 - cot x) + (cos x) / (1 - tan x)",
"29. ((sin theta)/(1+tan theta) + (cos theta)/(1+cot theta))(sin theta + cos theta) = 2 sin theta cos theta",
"30. (sec x - 1) / (sin x sec x) = tan (x/2)",
"31. ((cos theta)/(1+sin theta) + (1+sin theta)/(cos theta)) cot theta = 2 csc theta",
"32. (sin^6 theta - cos^6 theta)/(cos^4 theta - sin^4 theta) = (sin^2 theta) (cos^2 theta-csc^2 theta)",
"33. (2 sin theta - 7 - cos^2 theta)/(sin^2 theta + sin theta -12) = 1 + 1/(sin theta - 3)",
"34. (3 sec^2 theta + 5 tan theta - 5)/(6 tan^2 theta + tan theta  - 1) = 2 - 3/(cot theta + 2)",
"35. (cot^4 theta - csc^4 theta)/(2 cos^4 theta - 3 cos^2 theta-5) = 1/((sin^2 theta) ( 3 + 2 sin^2 theta))",
"36. (cos (x+y)) / (cos x sin y) = cot y - tan x",
"37. (tan^2 x+1) / (cot^2 x+1) = tan^2 x",
"38. sec^4 x - tan^4 x = (1+sin^2 x) / cos^2 x",
"39. sqrt ((1 - sin x) / (1+sin x)) = abs (cos x) / (1 + sin x)",
"40. 1 / sqrt (1+tan^2 x) = abs (cos x)",
"41. sec x - 2 tan^2 x = sec x - 2 sec^2 x + 2",
"42. cos 8x = cos^2 4x - sin^2 4x",
"43. (1 - cos 2x) / tan x = sin 2x",
"44. sin (pi/6 + x) = 1/2 (cos x + (sqrt 3) sin x)",
"45. sec^2 (x/2) = 2 / (1+cos x)",
"46. cos^2 (x/2) = (tan x + sin x) / (2 tan x)",
"47. csc 2x - cot 2x = tan x",
"48. 1 + cos x = sin x cot (x/2)",
"49. (1 - cos 2x) / sin 2x = tan x",
"50. (cos 2x - cos 4x) / (2 sin 3x) = sin x",
"51. (cos 8x + cos 4x) / (cos 8x - cos 4x) = - cot 6x cot 2x",
""
};

/*  6.17.13,  problems read from invtrig.mhw */
char *problems112[] = {
"1. arcsin 0",
"2. arccos 0",
"3. arccos(sqrt(3)/2)",
"4. arcsin(sqrt(3)/2)",
"5. arctan 1",
"6. arctan sqrt 3",
"7. arccos (1/2)",
"8. arcsin (sqrt(2)/2)",
"9. arctan(1/sqrt 3)",
"10. arccos 1",
"11. arctan 0",
"12. arcsin (1/2)",
"13. arccos(-(1/2))",
"14. arcsin(-sqrt(2)/2)",
"15. arctan(-1)",
"16. arctan(-sqrt 3)",
"17. arcsin(-(sqrt 3)/2)",
"18. arccos(-1)",
"19. arccos(- (sqrt 3)/2)",
"20. arcsin(-1)",
"21. arccos(cos (2pi/3))",
"22. arcsin(sin (pi/3))",
"23. cot(arctan(-1))",
"24. tan(arccot(-1))",
"25. arctan(tan(-pi/3))",
"26. arccos(cos(5pi/4))",
"27. tan (arcsin((sqrt 3)/2))",
"28. sin( arcsin (1/2))",
"29. arccot (cot(-7pi/3))",
"30. sin(arcsin(1/2) + arccos 0)",
"31. arcsin(sin(1/2))",
"32. sin(arcsin(-(sqrt 3)/2))",
"33. cos( arccos(1/2))",
"34. tan(arctan(1/pi))",
"35. sin(arccos (3/5))",
"36. cos(arctan(-1/3))",
"37. cos(arctan(-3))",
"38. cos(arctan5)",
"39. sin(arctan(12/5))",
"40. sin(2arccos(3/5))",
"41. sin(2arccos(3/sqrt 13))",
"42. tan (2arcsin(3/5))",
"43. cos(2arcsin(-5/13))",
"44. sin(2arctan(5/12))",
"45. tan ((1/2) arcsin(15/17))",
"46. cos((1/2) arcsin((sqrt 3)/5))",
"47. tan(arctan (3/4) - arcsin(1/2))",
"48. sin(arccos(1/2) + arcsin(1/2))",
"49. cos(arcsin(1/3) - arctan(1/2))",
"50. tan( arcsin(1/2) - arccos(1/3))",
"51. sin(2arccos x)",
"52. cos(2arcsin x)",
"53. csc(arccos x)",
"54. csc(arcsin x)",
"55. tan(2arccos x)",
"56. cos((1/2) arccos x)",
"57. cos(arcsin x - arccos x)",
"58. cot(arcsin((sqrt(x^2 -9))/x))",
""
};

/*  6.17.13,  problems read from eqsimple.mhw */
char *problems113[] = {
"1. sin x =0",
"2. sin x = 1/3",
"3. cos x =0",
"4. cos x = -8/9",
"5. tan x =0",
"6. tan x = 13",
"7. cot x =0",
"8. tan x = -5/4",
"9. sin x = 1",
"10. cos x =-1",
"11. cos x =1",
"12. cot x =1",
"13. cot x = 1/20",
"14. cot x = - 7/2",
"15. csc x = 42",
"16. sin x = (sqrt 3)/2",
"17. cos x = -(sqrt 2)/2",
"18. sec x = 2",
"19. sin x = - (sqrt 3)/2",
"20. sin x = - 1/2",
"21. tan x = 1",
"22. tan x = (sqrt 3)/3",
"23. sin x = -1",
"24. csc x = 2",
"25. sin x = sqrt 2",
"26. cot x = 1/sqrt 3",
"27. cot x = - sqrt 3",
"28. tan x = sqrt 3",
"29. (sqrt 3) tan x = 1",
"30. 1 + cos 4x = 0",
"31. 4 sec x = 8",
"32. (sqrt 3) tan (x/3) = 1",
"33. 2 cos 4x = - sqrt 2",
"34. sin (x - pi/2) = 1/2",
"35. sin (3x - pi/4) = 1",
"36. tan(pi x) = -sqrt 3",
"37. 2sin(x-1) = sqrt 2",
"38. 2sec x - 2 sqrt 2 =0",
"39. 2cos(x/3) =1",
"40. -2cos(4x + 2pi) = 1",
"41. 2 cot x - 1 = 5",
"42. 2cot(3x - pi/4) =2",
"43. 4cos^2 x - 3 =0",
"44. 3sec^2 x - 4 =0",
"45. 2sin^2 x =1",
"46. tan^2 x = 3",
"47. sin^2 x + 4 =5",
"48. cot^2 x = 1/3",
"49. 2sin^2 x - 1=0",
"50. sin x - (sqrt 3) cos x =0",
"51. sin x = - cos x",
"52. 2 - 8cos^2 x =0",
"53. tan^2 x = tan x",
"54. sin x = cos x",
"55. (sqrt 3) sin x - cos x =0",
"56. (sin x +1) tan x = 0",
"57. (2 sin x + 1) (2cos x + 3)=0",
"58. (cos x -1)(sin x + 1) =0",
"59. (sin 2x) (csc 2x - 2) =0",
"60. (3sin x - 3(sqrt 2)/2) (cos x - sqrt 2) =0",
"61. 2(cos^2 x - sin^2 x) = sqrt 2",
""
};

/*  6.17.13,  problems read from trigeqn.mhw */
char *problems114[] = {
"1. 1 + sqrt 2 sin theta = 0",
"2. 1 + cos x = 0",
"3. 1 - sin x = 0",
"4. 1 - sqrt 2 cos theta = 0",
"5. sin theta = cos theta",
"6. 4 sin^4 theta - 1 = 0",
"7. 16 cos^4 (theta/2) -9 = 0",
"8. 4 cos^2 2 theta - 1 = 0",
"9. sin x + cos x = 1",
"10. sqrt 3 sin x - cos x = 0",
"11. sin theta + 3 cos theta = 1",
"12. sin^2 theta = sin theta",
"13. 3 sin x cos x = sin x",
"14. cos^2 theta = cos theta",
"15. tan ^2 x + tan x = 0",
"16. tan theta = 2 sin theta",
"17. sin x = sin 2x",
"18. cos x = sin 2x",
"19. 3cos^4 x + 4cos^2 x =0",
"20. tan^2 t sin t = sin t",
"21. 2 sin^2 x = 1- 2 sin x",
"22. 2 sin^2 x = 3sin x -1",
"23. 2 cos^2 x +  cos x = 1",
"24. tan^2 x + 1 = 3tan x",
"25. 4 cos^2 theta = 7 cos theta + 2",
"26. 2sin^2 x + 6sin x - 3 = 0",
"27. 2 cos^2 x - 3cos x = -1",
"28. 2 cos^2 x = 3sin x + 3",
"29. 2sin^2 (x/2) - 3sin(x/2) + 1 = 0",
"30. 4cos^2 2x - 4cos 2x + 1 = 0",
"31. sin^2 theta - 2 sin theta + 1 = 0",
"32. 2 sin^2 theta - 3 sin theta + 1 = 0",
"33. 2 cos^2 theta + sqrt 3 sin theta - 2 = 0",
"34. 2sin x = cos 2x",
"35. cos x + 2cos^2 (x/2) =2",
"36. sec x + tan x = 1",
"37. cot theta - csc theta = 1",
"38. tan theta sec theta = sqrt 2",
"39. sec^2 2 theta - tan 2 theta = 1",
"40. sec^2 t - 2tan^2 t = 0",
"41. 1 - sin x = sqrt 3 cos x",
"42. sin x + 3 = -2csc x",
"43. sec^5 theta = 4sec theta",
"44. 2sin x tan x + tan x - 2sin x - 1 = 0",
"45. 3 sec theta = 4 cos theta",
"46. cot theta = sqrt 2 cos theta",
"47. tan 2 theta = 3 cot 2 theta",
"48. 2 (cos^4 theta + 1 - sin^4 theta) = 3",
"49. (cot theta + 1)(cos theta - sin theta) + sin theta  = (sqrt 2)/2",
"50. sin(u/2) = 1 - cos u",
"51. (sec 2 theta -1)(cos 2 theta + 1) = (sqrt 2)/2",
"52. sin 3x - sin x = 0",
"53. cos 5x + cos x = 0",
"54. sin 2x + sin 4x = 0",
"55. sin 3x - sin 2x = 0",
"56. sin 5x - sin 3x = sin x",
"57. cos 3x - cos x = sin x",
"58. 4 cos^2 theta + 4 cos theta  = 0",
"59. sqrt((csc theta + 1)/(csc theta - 1)) + sqrt((csc theta - 1)/(csc theta + 1)) = 2 sqrt 2",
""
};

/*  6.17.13,  problems read from comarith.mhw */
char *problems115[] = {
"1. i^2",
"2. i^3",
"3. i^4",
"4. i^5",
"5. i^17",
"6. i^1017",
"7. (3-i) + (12 + 7i)",
"8. (6-3i) - (84-6i)",
"9. 17i - (3-3i) - (6+4i)",
"10. (1/3 - (1/5)i) + (1/5 - (1/4)i)",
"11. sqrt(-49)",
"12. sqrt(-36)",
"13. sqrt(-64/36)",
"14. sqrt(-64)",
"15. sqrt(-4) sqrt(-9)",
"16. sqrt(-3) sqrt(-8)",
"17. sqrt(-3) sqrt(-10)",
"18. sqrt(-81)/sqrt(-4)",
"19. (5i)(4i)",
"20. (5i)(-6i)",
"21. (2i)(2-5i)",
"22. (-3i)(-1-7i)",
"23. (1+i)(3+8i)",
"24. (4-i)(8-6i)",
"25. (5-i)(5-6i)",
"26. (-2-3i)^2",
"27. (2+3i)^2",
"28. 5i/(3+4i)",
"29. -3i/(2-5i)",
"30. (-1+6i)/(7i)",
"31. 2/(7i)",
"32. (3+6i)/(1+8i)",
"33. (7+6i)/(4-9i)",
"34. (-5+7i)/(-1+i)",
"35. (1-i)/(1+i)",
"36. (sqrt 2 + 2i)(sqrt 2 - 2i)",
"37. (5 + sqrt(-2))(3 - sqrt(-8))",
"38. (1+i)^4",
"39. (1- (sqrt 3)i)/(sqrt 3 + i)",
"40. (sqrt 2)/(i^2 - i^3)",
"41. (a+b i)(a- b i)/(1-i)^4",
"42. 2i / (3 - 3i)",
"43. (1 + i)^3",
"44. (1 - i)^4",
"45. (7 - 7i)^2",
"46. (1+i)/i",
"47. (1 - (sqrt 3)i) (4 sqrt 3+4i)",
"48. (3+3i) (1+i)",
"49. (1+ (sqrt 3)i)/(sqrt 3 + i)",
"50. 8/(-1 + (sqrt 3) i)^3",
"51. (sqrt 2)/(i^2 + i^3)",
"52. 1/(-1 + i)^4",
"53. (a + b i)(a - b i)/(1-i)^4",
"54. i (i - 1) (sqrt 3+i)",
"55. (1 - i) (2 - 2i) (sqrt 3+4i)",
""
};

/*  6.17.13,  problems read from logfuncs.mhw */
char *problems116[] = {
"1. log (2, 1)",
"2. log (2, 1/2)",
"3. log (2, 32)",
"4. log (10, 10^5)",
"5. log (16, 8)",
"6. log (8, 1/16)",
"7. log (8, 16)",
"8. log (3, 9)",
"9. log (1/3, 9)",
"10. log (2, 4^(1/5))",
"11. log (5, 5)",
"12. log (10, 2) + log (10, 5)",
"13. log 6 - log 15+log 20",
"14. log (8, 80) - log (8, 5)",
"15. log (10, 50) - log (10, 5)",
"16. 2/3 log 27 + 1/3 log 8",
"17. 1/3 (2 log 8 - 6 log 3) - 2 log 2 + log 3",
"18. log(xy) + log(y)",
"19. log(x/y) + log(y)",
"20. log(u^5)",
"21. log( sqrt x)",
"22. log( root(5, x))",
"23. log(xyz) - log z",
"24. log(x/(yz))",
"25. log ((x^4 y) / z^2)",
"26. log ((2x+5) / x^5)",
"27. log ((x^3 y^2 z^(-1)) / (x y^4 z^(-2)))",
"28. log ((sqrt (x^2 - 1)) / x)",
"29. log sqrt (x / (y^2z^2))",
"30. log ((sqrt y) / (x^3 root (4, z)))",
"31. log sqrt ((x^2 - y^2) / (x+y))",
"32. log sqrt (x sqrt (y sqrt z))",
"33. log ( 10^x / (x (x^2+1)))",
"34. log (2, 2^(x+3) / 2^(x - 1))",
"35. log(x) + log(y) + log(z)",
"36. log(x)-log(y)",
"37. log(x^2) - log(y^4)",
"38. log(x) + log(y) - log(z)",
"39. 3 log(x) - log(y)",
"40. log(x) - (1/5) log(y)",
"41. log(x) + 2 log(y) - 3 log(z)",
"42. (1/4) (log(x) - log(y))",
"43. log (37) - log x",
"44. log (2x+2) - 2 log (x+1)",
"45. log x + log (7y)",
"46. log (x^2 - 9) - log (x - 3)",
"47. log 2^x - x log 2",
"48. log (x^2 - 1) + log y - log x",
"49. 2 ln x - 4 ln (1/y) + 3 ln (xy)",
"50. log (x/4) + log (y/3) - log (z/2)",
"51. 1/2 log (x^2 - 1) - 1/2 log (x^2+1)",
"52. log (x^2 y^3) - 2 log (x sqrt y) - 3 log (x/y)",
"53. 1/2 (log (x^2+4x+4) - log (x+2))",
"54. 3 (2 log y + log z) - 4 log x",
""
};

/*  6.17.13,  problems read from basechng.mhw */
char *problems117[] = {
"1. log (3, 10^5)",
"2. log (5, 92)",
"3. log(4, 23)",
"4. log (11, 3)",
"5. log (4, 10 pi)",
"6. log(pi, pi)",
"7. log(9, 1)",
"8. log (3, pi)",
"9. log  (3, e)",
"10. log (1/2, 6)",
"11. log(1/4, 1/4)",
"12. log(2, 1/200)",
"13. log (1/3, 6)",
"14. log (3, 270)",
"15. log (3, 10)",
"16. log (2, 64)",
"17. log(12, 435)",
"18. log(pi, pi^23)",
"19. log (7, 14)",
"20. log (9, 3/2)",
"21. log (9, 2/3)",
"22. log (8, 30)",
"23. log (7, 50)",
"24. log (5, 1/2)",
"25. log (4, 7)",
"26. log (2, 16/25)",
"27. log (6, 1/2)",
"28. log (sqrt 3, 1/9)",
"29. log (5, 6)",
"30. log (7, 124)",
"31. log (8, 4578)",
"32. log (a, 2)",
"33. log (1/3, 2/3)",
"34. log (8, 2)",
"35. log (4, 12)",
"36. log (6, 5)",
"37. log (5, 1/2)",
"38. log (12, 265)",
"39. log (50, 1000)",
"40. log (500, 250)",
"41. log (2, 10)",
"42. log (12, 100)",
"43. log (7,5)",
"44. log (2, 75)",
"45. log (5, 135)",
"46. 2/5 log (8, 127)",
"47. log (sqrt 3, 27)",
"48. log (9, 10^sqrt (23))",
"49. log (2, 16) / log (5, 4)",
"50. (2 log (6, 3)) / (3 log (6, 2))",
"51. log (7, 243) / log (7, 3)",
"52. log (6, 5) - log (10, 15)",
"53. log (3, 7) log (3, 8/3)",
""
};

/*  6.17.13,  problems read from explogs.mhw */
char *problems118[] = {
"1. 2^(log(2, 4x))",
"2. e^ln(x^2)",
"3. 10^(log x - log y)",
"4. 2^log(2, 2^sqrt 5)",
"5. 10^log(10000)",
"6. e^(ln sqrt x)",
"7. e^(ln x/2)",
"8. e^( 2 ln x)",
"9. 10^(2 log x - 3 log y)",
"10. e^(-ln x)",
"11. e^(2 ln x + 5 ln y)",
"12. log(2, 32^x)",
"13. ln(e^(x^2 + 1))",
"14. ln(xe^x^2)",
"15. ln(x^2 e^x^2)",
"16. log(10^x/x)",
"17. ln(e^x/x)",
"18. ln(e^x/x^3)",
"19. ln(e^x^2/x^3)",
"20. ln (ln(e^x^2)-1)",
"21. e^(1/x ln 2)",
"22. e^(1/x ln 2^x)",
"23. (49)^(log (7, 2))",
"24. (49)^(1/ log (8,7))",
"25. ln (1/2 e^(x - 1))",
"26. ln (e^(x^3) / (y^2 (x - 1)))",
"27. 5^( log (1/5, 2x^2))",
"28. 5^( 1/2 log (sqrt 5, a))",
"29. 2^(2 (log (2, x)+2))",
"30. 25^(1/ log (6,5))",
"31. log (root (5, 5^(x^2 - 10x)))",
"32. 10^(1 - log 2)",
"33. 10^log (x^2 - 21)",
"34. log (3, x^log (3, x))",
"35. 3^(3 / log (sqrt 6, 3))",
"36. 9^log (1/3, x+1)",
"37. 81^(1 / log (5, 9))",
"38. 8^log (4, 9)",
"39. 7^(4 log (49, a))",
"40. 2^log (root (4, 2),a)",
"41. 36^ log (6, 5)",
"42. 3^ log (27, a^2+1)",
"43. x^(2 / log (3,x))",
"44. log (2, log (2, a^log (a, 4)))",
"45. log(10^100) + 10^log(100)",
"46. ln(x^x)",
"47. log(x^x^2)",
"48. ln(3e^x^2)-ln(log(1000))",
"49. 10^(2 log (x+y)) - 10^(2 log(x-y))",
"50. ln (e^(ln y))",
""
};

/*  6.17.13,  problems read from logpower.mhw */
char *problems119[] = {
"1. log(10^100) + 10^log(100)",
"2. log(x^2) - log(y^4)",
"3. ln(x^x)",
"4. ln(e^(x^2 + 1))",
"5. log(x^x^2)",
"6. ln(e^x^2)/x^3",
"7. ln(e^x)/x",
"8. ln (u/(root(5, 3-u)))",
"9. log (2, 2^(x - 1))",
"10. ln (root(4, x^2-y^2))",
"11. ln (x sqrt(x/y))",
"12. ln (x^2-1) - ln (x - 1)",
"13. 2 log (6, sqrt (6x)) - log (6, x)",
"14. log(sqrt x - 2) + log(sqrt x + 2)",
"15. ln(3e^x^2)-ln(log(1000))",
"16. log ((x^5 y^3 z^(-1)) / (x y^5 z^(-2)))",
"17. log (2, log (2, a^log (a, 4)))",
"18. log sqrt (x sqrt (y sqrt z))",
"19. log (2, 2^(x-1) / 2^(x +1))",
"20. 1/2 log (x^2 - 1) + 1/2 log (1/(x-1))",
"21. log (x^2 - 16) - log (x - 4)",
"22. 1/2 (log (x^2+4x+4) - log (x+2))",
"23. log(x^2-1) + log(x+1) - log(x^3+1)",
"24. log(sqrt(x-1) + 1) +  log(sqrt(x-1)-1)",
"25. log (x^2 y^3) + 2 log (x sqrt y) + 3 log (x/y)",
"26. log (x^log x)",
"27. log (x - 4) - log (3x - 12) + log (1/x)",
"28. 2 log(x+a) - log(x^2-a^2)",
"29. 10^log(5-x^2) + 10^log(3x-5)",
"30. 5^log (5, x^3)",
"31. 10^ (2 log (x+y)) - 10^(2 log(x-y))",
"32. log (2, 4^x) - log (2, 2^(x-3))",
"33. 10^(2 log x +2 log y)",
"34. e^(2 ln x -3 ln y)",
"35. ln(ln(e^x^2))",
"36. e^(1/x ln 3^x^2)",
"37. (49)^(log (7, x))",
"38. 5^( log (1/5, 2x^3))",
"39. log (root (5, 5^(x^2 - 10x)))",
"40. log (3, x^log (3, x))",
"41. 3^ log (27, x^2)",
"42. 9^log (1/3, x^2-1)",
"43. (1/7)^(4 log (49, a))",
"44. 2^log (root (4, 2),x)",
"45. 2^ log x^2 - 4^(log x +1)",
"46. log (2, log (2, log (2, a^(2 log (a, 4)))))",
"47. ln(root(4, (x^2+1)/(x^2 (x^2-1)^3)))",
"48. ln (sqrt (x root(3, y root(4, z))))",
"49. log (((x^2+5x+2)/(x^3-2))^(1/5))",
"50. ln ((3x sqrt (1-x))/((x-3)^4 (x+3)^2))",
""
};

/*  6.17.13,  problems read from logeqn.mhw */
char *problems120[] = {
"1. log (9, 81) = x",
"2. log (1/2, x) = 5",
"3. log (sqrt 5, x) = -4",
"4. log sqrt (x^2 - 1) = 2",
"5. log (2x - 5) = log 8",
"6. log x + log 8 = 1",
"7. ln x = 1/2 ln x",
"8. log(x-9) + log 100 x = 3",
"9. ln (x+1) / ln (x - 1) = 2",
"10. log (4, x+6)+ log (4, x - 6) = 3",
"11. log(6x+5) - log 3 = log 2 - log x",
"12. log(3x+7) = 2",
"13. 2 log(x+1) = 1",
"14. ln x + ln(x+2) = 1",
"15. ln 2x + ln(3x-e) - 2 = ln 8",
"16. 2 log x - 2 = log(1-x)",
"17. 3 log x - 3 log(x+1) = 9",
"18. log x + log (x+1) = log 12",
"19. ln (2x+3)+ln x = ln e",
"20. log(x^2 + 3x) = 1",
"21. log (5, x) + log (5, 2) = 2",
"22. log (2, x+1) + log (2, x+4) = 2",
"23. ln (ln x) = 0",
"24. log (log x) = 2",
"25. ln (x^3+3) = ln 4+ ln x",
"26. log (10, x^2 - 1) - log (10, x+1) = 1",
"27. log(x^3 + 1) - 1 = log(x+1)",
"28. (log x)^3 = log x^2",
"29. log x^2 = (log x)^2",
"30. log log x = 1",
"31. log(2x-1) + log(x-1) = 2 - log(3x+1)",
"32. 2 log(2x-5) + log(x+7) = 1",
"33. log(5-x^2) + log(3x-5) = 0",
"34. 3 log x + log(4-3x) = 0",
"35. ln (x^2+1) - ln (x - 1) = 1+ ln (x+1)",
"36. 3 log x = log (3x)",
"37. log (x^2 - x) = log x + log (x - 1)",
"38. log (2, log (4, x)) = -1",
"39. log(sqrt x - 2) + log(sqrt x + 2) = 1",
"40. log (10, 8) + log (10, x) + log (10, x^2) = 3",
"41. log (2, 2^(x - 1)) = 3",
"42. log (5, x^3) = 6",
"43. log(sqrt(x-1) + 1) + 2 log(sqrt(x-1)-2) = 2 log 2",
"44. log (x^log x) = 16",
"45. 3( log(2, x))^2+log (2, x) - 2 = 0",
"46. log (x - 4) - log (3x - 10) = log (1/x)",
"47. abs (log (4, x)) = 2",
"48. 2 log x + log a = 0",
"49. 3 log(x-1) = 2 log(a+1)",
"50. 2 log x - 1 = log(x^2-a^2)",
"51. a = ln(2 - sqrt(4-x^2)) - ln x",
"52. a = ln x + ln(2-x)",
"53. a = 2 ln x - ln(2x-1)",
"54. a = ln(x + sqrt(x^2 + 4))",
""
};