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ELF	>�/@@1. (x^3yz^2)(xy^2z^3)2. (2x^2)(3x^3)(5x^5)3. (-x^3y^5)^74. (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)^211. (x - y)^2+17 (x - y) +1612. (x-y)^2 - 6(x-y) + 913. (x+a)^3 + (x-a)^314. x^2+11x+1815. 3x^2+24x+3616. 10x^2 - 8x - 217. x^4 - 3x^2 - 418. (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/x37. 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 ) + x45. (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)))1. (x^2 + y^2)(x- y)(x+y) + y^4 = x^42. (x^2x^2 + x^4)x^4 + x^8= 3x^83. (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+56. (x^2x^2 + x^4)x^4 - x^8 = x^87. (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)^29. ((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-112. (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))= -215. (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)/x20. [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+y23. (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+526. (5/x+8/(2x+1)) / (6 /(2x+1) - 3/x)= -(18x+5)/327. (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-y29. (ab+b^2)/3 (3a/b^3) + (a+b)/b = ((a+b)/b)^230. (x-y)/(4y) ((8y^2)/(x^2 -xy)) - 3/x^2 = (2xy-3)/x^231. 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)) =137. (2x+1-1/(1-2x))/(2x-4x^2/(2x-1))= -2x38. (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/a40. ((5x+y)/(x^2-5xy) + (5x-y)/(x^2 +5xy))( (x^2 -25y^2)/(x^2+y^2))= 10/x41. (a+b -2ab/(a+b))/( b/a+ (a-b)/(a+b))= a42. (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^244. (p/q+q/p)^2 - (p/q- q/p)^2 = 445. (((x+y)/(xy))^2) / (1/x^2 +1/y^2 + (2/(x+y))(1/x+1/y))=146. ( (1-a)(1-b)/(1+ab) -1)^2 + (1-a^2)(1-b^2)/(1+ab)^2=147. ((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)=11. 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)1. (sin (-x)) / cos (-x) = - tan x2. sec (-x) = sec x3. cot u sec u sin u = 14. sqrt (tan^(2) x +1) = abs(sec x)5. (sin^2 x + cos^2 x)^5 = 16. 1 / ((sec^3 x ) cos^4 x) = sec x7. (sin x) (csc x - sin x) = cos^2 x8. (1 / csc^2 x) + (1/ sec^2 x) = 19. (1 / sec^2 t) = 1 - (1 / csc^2 t)10. (sin x + cos x)^2 + (sin x - cos x)^2 = 211. (1+cos x)(1 - cos x) = sin^2 x12. (sin x +cos x)^2 = 1+2(sin x) cos x13. (1+tan^2 x) / tan^2 x = csc^2 x14. tan x+1 = (sec x)(sin x+cos x)15. (cos x) / (1 - sin^2 x) = sec x16. (sin x) / csc x + (cos x) / sec x = 117. (1+sec x) / csc x = sin x + tan x18. sin^4 x + cos^4 x = 1 - 2 (sin^2 x) cos^2 x19. sin^2 t + tan^2 t + cos^2 t = sec^2 t20. cos^4 x + 2(cos^2 x) sin^2 x + sin^4 x = 121. (cos^2 t)/sin t + sin t = csc t22. cot^2 x sin^2 x = 1-sin^2 x23. (1- cos^2 y)/((1-sin y)(1+sin y)) = tan^2 y24. ((cot u) cos u) / (csc^2 u - 1) = sin u25. (sin x + tan x) / (1 + sec x) = sin x26. sin x = ((tan x) cot x) / csc x27. (tan x) (tan x + cot x) = sec^2 x28. (1 + sin x) / cos x = (cos x) / (1 - sin x)29. (tan^2 x) cos^2 x = 1 - cos^2 x30. 1 / (csc x - sin x) = (sec x) tan x31. (cos x)/(csc x + 1) + (cos x)/(csc x-1) = 2 tan x32. (csc^4 x-1)/cot^2 x = 2 + cot^2 x33. ((1 - cos x) / sin x) + (sin x) / (1 - cos x) = 2 csc x34. sec x - cos x = (1 - cos^2 x) / cos x35. (csc x) / (tan x + cot x) = cos x36. (1+csc x) / (cot x + cos x) = sec x37. (2 cos^2 x) - 1 = 1 - 2 sin^2 x38. (2 sin^2 x - 1) / (sin x+cos x) = sin x - cos x39. (tan x - 1)^2 = sec^2 x - 2 tan x40. cos x + (cos x) tan^2 x = sec x41. (sin x) (1+cos x) = (sin^3 x) / (1 - cos x)42. (sin u)/(1-cos^2 u) = csc u43. cot x + sec x = (cos x + tan x)/sin x44. ((cot x) / (1 - tan x)) + (tan x) / (1 - cot x) = 1+(sec x) csc x45. (tan x - tan y) / (cot x - cot y) = -(tan x)tan y46. (tan x) / (sec x - 1) = (sec x + 1) / tan x47. (tan x - 1) / (tan x +1) = (1 - cot x) / (1 + cot x)48. sec^2 u + csc^2 u = sec^2 u csc^2 u49. (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 u52. tan^2 x - sin^2 x = (tan^2 x) sin^2 x53. sin^4 x - cos^4 x = sin^2 x - cos^2 x54. 1 - 2 cos^2 x + cos^4 x = sin^4 x55. sec^4 x - tan^4 x = 1 + 2 tan^2 x56. sec^2 x + csc^2x = (sec^2 x) csc^2 x57. sin^4 x - 2 sin^2 x + 1 = cos^4 x58. sin^4 x + cos^2 x = sin^2 x+cos^4 x59. (sin x)/(1-cos x) = (1+cos x)/sin x1. sin(x + 2 pi) = sin x2. cos(x + 2 pi) = cos x3. tan(x + pi) = tan x4. cot(x + pi) = cot x5. cos(x+2 m pi) = cos x6. sin(x + 2 m pi) = sin x7. cot (x + m pi) = cot x8. tan( x+ m pi) = tan x9. tan(x + pi/2) = -cot x10. cos (pi/2 + x) = - sin x11. (sin (x+pi/2)) / cos (x+pi/2) = - cot x12. cot (pi/2+x) = - tan x13. sec (pi/2+ x) = - csc x14. cos (x - pi) = - cos x15. sin (pi+x) = - sin x16. cos (x+pi) = - cos x17. cos (pi - x) = - cos x18. tan (pi - x) = - tan x19. sin (x - pi) = - sin x20. csc (pi - x) = csc x21. cos (3 pi/2 - x) = - sin x22. sin (3 pi/2 - x) = - cos x23. tan (3 pi/2 - x) = cot x24. 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 x27. 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) = 030. 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 y33. sin (x+y) + sin(x - y) = 2 sin x cos y34. cos (x+y) cos (x - y) = cos^2 x - sin^2 y35. sin(x+y) - sin (x - y) = 2 cos x sin y36. cos x cos ( x - y) + sin x sin (x - y) = cos y37. (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 y40. (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 y42. 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) = 1/21. (sin x + cos x)^2 = 1 + sin 2x2. (sin x - cos x)^2 = 1 - sin 2x3. sin^2 x = (1/2) (1- cos 2x)4. sin 2x = (2 tan x) / sec^2 x5. 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 2x8. 2 cot(2 theta) = cot theta - tan theta9. 1- cos 2x = tan x sin 2x10. cos 4 theta = 2 cos^2 2 theta - 111. (sin 2x) / (1+cos 2x) = tan x12. 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 2t15. (1+sin 2x+cos 2x) / (1 + sin 2x - cos 2x) = cot x16. cos 2x = cos^4 x - sin^4 x17. (tan x) sin 2x = 1 - cos 2x18. (1 + 2 cos x)^2 = 3 + 4 cos x + 2 cos 2x19. sin^4 x + cos^4 x = (1 + cos^2(2x)) / 220. (sin^2 x) cos^2 x = 1/8 (1 - cos 4x)21. cos 4u = 1 - 8 (sin^2 u) cos^2 u22. cos 4x = 8 cos^4 x - 8 cos^2 x + 123. sin 4x = 4 (sin x) cos^3 x - 4 (sin^3 x) cos x24. 2 sin^2 (2x) + cos 4x = 125. sin 4x = (cos x) (4 sin x - 8 sin^3 x)26. (1 - cos 4x) (2 + tan^2 x + cot^2 x) = 827. 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) / 233. 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 2t38. 2 csc 2x = (1+tan^2 x)/tan x39. 2 csc 2x = tan x + cot x40. csc 2x = 1/2 (csc x) sec x41. sec^2 x = (sec 2x) (2- sec^2 x)42. tan x = csc 2x - cot 2x43. ((csc^2 x) sec^2 x) / (cot^2 x - tan^2 x) = sec 2x44. (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 4x47. cos 6x = 32 cos^6 x - 48 cos^4 x + 18 cos^2 x - 148. 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 - 150. (cot^2 theta + 1)/(cot^2 theta-1) = sec 2 theta51. (sin 3t)/cos t + (cos 3t)/sin t = 2 cot(2t)52. cos 8x = cos^2 4x - sin^2 4x53. cos 2x = cos^4 x - sin^4 x54. (1 - cos 2x) / tan x = sin 2x55. sin 3x = 3 sin x cos^2 x -  sin^3 x56. csc 2x - cot 2x = tan x57. (1 - cos 2x) / sin 2x = tan x58. cot x - tan x = (4 cos^2 x - 2) / sin 2x59. ((1 - cot x) / csc x)^2 = 1 - sin 2x60. (cos 2x - cos 4x) / (2 sin 3x) = sin x61. tan^2 x - cot^2 x = - 4 cot 2x csc 2x62. 1 - 4 sin^4 x = 2 cos 2x - cos^2 2x1. 2 sin(x/2) cos(x/2) = sin x2. 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 x6. cos x cot (x/2) sec^2 (x/2) = 2 cot x7. tan(pi/4 + theta/2) = sec theta + tan theta8. 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 x11. 2 cos^2(x/2) = (sin^2 x)/(1-cos x)12. cot(pi/4 + theta/2) + tan theta = sec theta13. 2 sin^2 (x/2) + cos x = 114. 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 x18. cos x = cos^4 (x/2)  - sin^4 (x/2)19. 1 - 4sin^4 (x/2) = 2 cos x - cos^2 x20. sin^4 (x/2)  + cos^4 (x/2)  = (1 + cos^2 x) / 221. cos 2x = 8 cos^4 (x/2)  - 8 cos^2 (x/2)  + 122. tan (x/2)  = csc x - cot x23. tan(x/2) = (1-cos x)/sin x24. 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) - 129. tan^2(x/2) -2 csc x tan(x/2) +1 = 030. cos^4 (x/2) - sin^4 (x/2) = cos x31. 4 (sin^6 (x/2)  + cos^6 (x/2)) = 4 - 3 sin^2 x32. cot x = (cot (x/2) - tan (x/2)) / 233. cot x = (cot^2(x/2) - 1)/(2 cot(x/2))34. cot (x/2) = csc x + cot x35. 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 x40. (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)  - 142. tan(3pi/4 - theta/2) + tan theta + sec theta = 043. (sin 2 theta + 2 sin theta)/(sin 2 theta - 2 sin theta) + cot^2(theta/2) = 044. 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) + 149. (sec x - 1)/(sin x sec x) = tan (x/2)1. sin 4x sin 5x2. sin theta sin 2 theta3. sin theta sin 3 theta4. sin theta sin 7 theta5. sin (deg (15)) sin(deg (45))6. sin (deg (105)) sin (deg (165))7. 2 sin 5x sin x8. sin 3x sin (-2x)9. sin 2x sin 3y10. sin 4x sin x11. sin 5x sin x12. sin (x+y) sin(x-y)13. sin 2x sin 6x14. cos (deg (15)) sin (deg (15))15. sin theta cos 5 theta16. sin theta cos 3 theta17. sin theta cos 2 theta18. sin 4x cos 5x19. 6 sin (pi/4) cos (pi/4)20. 4 sin (pi/3) cos (5 pi/6)21. sin x cos y22. sin 3x cos x23. sin 4x cos x24. sin 5x cos x25. 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 3x29. sin (- 4x) cos 8x30. cos 3x sin 9x31. cos x cos y32. cos x cos 2x33. cos 4x cos 5x34. cos 5x cos x35. cos 4x cos 12x36. cos 4x cos 14x37. cos (- 4x) cos 6x38. cos theta cos 2 theta39. 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 y44. cos 7x sin x + cos x sin 7x45. cos x cos (x/2) sin (3x/2)46. 4 sin x cos (x/2) sin (3x/2)47. sin 2x sin 4x sin 6x48. cos x cos 2x cos 3x49. csc x sec x1. sin(deg(70))-sin (deg(110)) = 02. (cos x - cos 5x) ( cos x+cos 5x) = sin 4x sin 6x3. 2 sin x cos (x+y) = sin (2x+y) - sin y4. sin(pi/3 + theta) - sin(pi/3 - theta) = sin theta5. sin(theta + pi/4) + cos(theta + pi/4) = sqrt 2 cos theta6. (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 theta8. cos (pi/6+x) cos (pi/6 - x) - sin (pi/6+x) sin (pi/6 - x) = 1/29. sin(x+y)sin(x-y)= sin^2 x - sin^2 y10. cos(x+y)cos(x-y)= cos^2 x - sin^2 y11. sin(x+y)sin(x-y)= cos^2 y - cos^2 x12. (sin(deg(140))-sin (deg(20))) / (cos(deg(140))+cos (deg(20))) = sqrt 313. (cos(deg(50))-cos (deg(10))) / (sin (deg(10))-sin (deg(50))) = (sqrt 3)/314. (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 x16. 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 x19. (cos 2x - cos 6x) / (sin 6x - sin 2x) = tan 4x20. (cos 3x+cos x) / (sin 3x+sin x) = cot 2x21. (cos x-cos 5x) / (sin x cos x) = 4sin 3x22. (sin 6y+sin 4y) / (sin y sin 5y) = 2 cot y23. (cos 5x - cos 7x) / (sin 7x - sin 5x) = tan 6x24. (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 2x27. (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 5x30. (sin 3x+cos 3x) / (cos x- sin x) = 1 + 2 sin 2x31. (sin 2x+sin 2y) / (cos 2x+cos 2y) = tan (x+y)32. (sin 5x+sin 3x) / (sin 5x - sin 3x) = tan (4x) / tan x33. (sin x+sin 2x+sin 3x) / (cos x+cos 2x+cos 3x) = tan 2x34. (sin 2x - sin 3x+sin 4x) / (cos 2x - cos 3x+cos 4x) = tan 3x35. (sin x+sin 3x+sin 5x) / (cos x+cos 3x+cos 5x) = tan 3x36. (cos x+cos 4x+cos 7x) / (sin x+sin 4x+sin 7x) = cot 4x37. (cos 8x + cos 4x) / (cos 8x - cos 4x) = - cot 6x cot 2x38. cos(2 theta - pi/4) - cos(2 theta + pi/4) = sqrt 2 sin 2 theta39. (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 2x42. cos y + cos 2y + cos 3y = (1+ 2cos y) cos 2y43. (sin u - sin 7u) / (2sin^2 (2u) -1) =  2 sin 3u44. (sin u - sin 3u) / (sin^2 u -cos^2 u) =  2 sin u45. (sin 2x)/sin x - (cos 2x)/cos x = sec x46. (2 sin 2x)/(sin 3x + sin x) = sec x47. (cos v+cos u) / (sin v + sin u) = cot ((u+v)/2)1. (sin theta cot theta  + cos^2 theta)/(1+cos theta)2. (csc^2 theta - cot^2 theta)/sec^2 theta3. 1 - 8 (sin^2 theta) cos^2 theta4. (sec theta tan theta - sin theta)/sin^3 theta5. cos^2 theta - cos 2 theta6. 1/(sin theta cos theta) - (cos theta)/sin theta7. (csc theta cot theta - cos theta)/cos theta8. (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 2theta15. (sin 2theta)/(2sin theta)16. (tan theta + 1)(sin theta - cos theta) + cos theta17. 2 (sin theta)/(sec theta -1) + 2 (sin theta)/(sec theta + 1)18. cos^3 theta + sin^2 theta cos theta19. (tan theta)/sec (-theta)20. 1 + (cot theta + csc theta)^2 - 2 (cos theta)/sin^2 theta21. (cos^4 theta + 1 - sin^4 theta) sec^2 theta22. (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 theta25. (tan theta + cot theta)^2 cos^2 theta - 126. (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 theta29. ((csc theta + cot theta)^2 + 1)/ (sec theta csc theta + sec theta cot theta)30. 2sin theta tan theta + tan theta - 2sin theta - 131. (sec theta - cos theta)/ tan theta32. (2 + sec^2 theta) tan^4 theta + 3 sec^2 theta - 233. 1 - 3 sin^2 theta cos^2 theta - sin^6 theta34. 1/(1-sin theta) + 1/(1 + sin theta)35. tan theta cos theta csc theta36. csc theta cot theta - cos theta - cos theta cot theta37. tan 2 theta + 3 cot 2 theta38. cos theta tan theta + sin^2 theta - 1 + sin theta39. csc theta cos^2 theta + sin theta40. (cot theta + 1)(cos theta - sin theta) + sin theta41. (1-cos theta)(csc theta + cot theta)42. cos theta + sin theta tan theta43. tan^2 theta - sin^2 theta44. sqrt((csc theta + 1)/(csc theta - 1)) + sqrt((csc theta - 1)/(csc theta + 1))45. 2sin theta cos^3 theta + 2sin^3 theta cos theta46. (cos theta sec theta)/tan theta47. 4 sin^2 theta sec^2 theta - 4 cos^2 theta tan^2 theta - cos^4 theta - 2 sin^2 theta +148. ((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 theta50. (tan 2theta)/(tan 4theta - tan 2theta)1. sin^2 x cot^2 x + cos^2 x tan^2 x = 12. (sin x + cos x)^2 - (sin x - cos x)^2 = 4 sin x cos x3. 1 - 2 cos^2 x + cos^4 x = sin^4 x4. (sin theta cot theta  + cos^2 theta)/(1+cos theta) = cos theta5. (sec theta tan theta - sin theta)/sin^3 theta = sec^2 theta6. (csc theta cot theta - cos theta)/cos theta = cot^2 theta7. ((1+sin x) / (1+cos x)) ((1+sec x) / (1+csc x)) = tan x8. 3/(1-cos theta) - 3/(1+cos theta) = 6 cot theta csc theta9. (1 - cos x) / sin x = (sin x) / (1+cos x)10. (csc theta -1)(sin theta + 1) = cos theta cot theta11. (tan theta + 1)(sin theta - cos theta) + cos theta = sin theta tan theta12. 1- (sin^2 x) / (1 + cos x) = cos x13. (1 - tan x) (1 - cot x) = 2 - sec x csc x14. 2 (sin theta)/(sec theta -1) + 2 (sin theta)/(sec theta + 1) = 4 cot theta15. (sec theta - tan theta)^2 (1+ sin theta)^2 + sin^2 theta = 116. (cos^4 theta + 1 - sin^4 theta) sec^2 theta = 217. 1 + (cot theta + csc theta)^2 - 2 (cos theta)/sin^2 theta = 2 csc^2 theta18. (sin^3 theta - cos^3 theta)/(1+sin theta cos theta)+cos theta = sin theta19. 1 - 3 sin^2 theta cos^2 theta - sin^6 theta = cos^6 theta20. (tan theta + cot theta)^2 cos^2 theta - 1 = cot^2 theta21. 1/ (1+sin x) + 1/ (1 - sin x) = 2 sec^2 x22. ((csc theta + cot theta)^2 + 1)/ (sec theta csc theta + sec theta cot theta) = 2 cot theta23. (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 theta25. (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 x27. (sin^2 theta sec^2 theta - cos^2 theta tan^2 theta)/(2 sin^2 theta - 1 + cos^4 theta) = sec^2 theta28. 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 theta30. (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 theta32. (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 x37. (tan^2 x+1) / (cot^2 x+1) = tan^2 x38. sec^4 x - tan^4 x = (1+sin^2 x) / cos^2 x39. 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 + 242. cos 8x = cos^2 4x - sin^2 4x43. (1 - cos 2x) / tan x = sin 2x44. 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 x48. 1 + cos x = sin x cot (x/2)49. (1 - cos 2x) / sin 2x = tan x50. (cos 2x - cos 4x) / (2 sin 3x) = sin x51. (cos 8x + cos 4x) / (cos 8x - cos 4x) = - cot 6x cot 2x1. arcsin 02. arccos 03. arccos(sqrt(3)/2)4. arcsin(sqrt(3)/2)5. arctan 16. arctan sqrt 37. arccos (1/2)8. arcsin (sqrt(2)/2)9. arctan(1/sqrt 3)10. arccos 111. arctan 012. 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))1. sin x =02. sin x = 1/33. cos x =04. cos x = -8/95. tan x =06. tan x = 137. cot x =08. tan x = -5/49. sin x = 110. cos x =-111. cos x =112. cot x =113. cot x = 1/2014. cot x = - 7/215. csc x = 4216. sin x = (sqrt 3)/217. cos x = -(sqrt 2)/218. sec x = 219. sin x = - (sqrt 3)/220. sin x = - 1/221. tan x = 122. tan x = (sqrt 3)/323. sin x = -124. csc x = 225. sin x = sqrt 226. cot x = 1/sqrt 327. cot x = - sqrt 328. tan x = sqrt 329. (sqrt 3) tan x = 130. 1 + cos 4x = 031. 4 sec x = 832. (sqrt 3) tan (x/3) = 133. 2 cos 4x = - sqrt 234. sin (x - pi/2) = 1/235. sin (3x - pi/4) = 136. tan(pi x) = -sqrt 337. 2sin(x-1) = sqrt 238. 2sec x - 2 sqrt 2 =039. 2cos(x/3) =140. -2cos(4x + 2pi) = 141. 2 cot x - 1 = 542. 2cot(3x - pi/4) =243. 4cos^2 x - 3 =044. 3sec^2 x - 4 =045. 2sin^2 x =146. tan^2 x = 347. sin^2 x + 4 =548. cot^2 x = 1/349. 2sin^2 x - 1=050. sin x - (sqrt 3) cos x =051. sin x = - cos x52. 2 - 8cos^2 x =053. tan^2 x = tan x54. sin x = cos x55. (sqrt 3) sin x - cos x =056. (sin x +1) tan x = 057. (2 sin x + 1) (2cos x + 3)=058. (cos x -1)(sin x + 1) =059. (sin 2x) (csc 2x - 2) =060. (3sin x - 3(sqrt 2)/2) (cos x - sqrt 2) =061. 2(cos^2 x - sin^2 x) = sqrt 21. 1 + sqrt 2 sin theta = 02. 1 + cos x = 03. 1 - sin x = 04. 1 - sqrt 2 cos theta = 05. sin theta = cos theta6. 4 sin^4 theta - 1 = 07. 16 cos^4 (theta/2) -9 = 08. 4 cos^2 2 theta - 1 = 09. sin x + cos x = 110. sqrt 3 sin x - cos x = 011. sin theta + 3 cos theta = 112. sin^2 theta = sin theta13. 3 sin x cos x = sin x14. cos^2 theta = cos theta15. tan ^2 x + tan x = 016. tan theta = 2 sin theta17. sin x = sin 2x18. cos x = sin 2x19. 3cos^4 x + 4cos^2 x =020. tan^2 t sin t = sin t21. 2 sin^2 x = 1- 2 sin x22. 2 sin^2 x = 3sin x -123. 2 cos^2 x +  cos x = 124. tan^2 x + 1 = 3tan x25. 4 cos^2 theta = 7 cos theta + 226. 2sin^2 x + 6sin x - 3 = 027. 2 cos^2 x - 3cos x = -128. 2 cos^2 x = 3sin x + 329. 2sin^2 (x/2) - 3sin(x/2) + 1 = 030. 4cos^2 2x - 4cos 2x + 1 = 031. sin^2 theta - 2 sin theta + 1 = 032. 2 sin^2 theta - 3 sin theta + 1 = 033. 2 cos^2 theta + sqrt 3 sin theta - 2 = 034. 2sin x = cos 2x35. cos x + 2cos^2 (x/2) =236. sec x + tan x = 137. cot theta - csc theta = 138. tan theta sec theta = sqrt 239. sec^2 2 theta - tan 2 theta = 140. sec^2 t - 2tan^2 t = 041. 1 - sin x = sqrt 3 cos x42. sin x + 3 = -2csc x43. sec^5 theta = 4sec theta44. 2sin x tan x + tan x - 2sin x - 1 = 045. 3 sec theta = 4 cos theta46. cot theta = sqrt 2 cos theta47. tan 2 theta = 3 cot 2 theta48. 2 (cos^4 theta + 1 - sin^4 theta) = 349. (cot theta + 1)(cos theta - sin theta) + sin theta  = (sqrt 2)/250. sin(u/2) = 1 - cos u51. (sec 2 theta -1)(cos 2 theta + 1) = (sqrt 2)/252. sin 3x - sin x = 053. cos 5x + cos x = 054. sin 2x + sin 4x = 055. sin 3x - sin 2x = 056. sin 5x - sin 3x = sin x57. cos 3x - cos x = sin x58. 4 cos^2 theta + 4 cos theta  = 059. sqrt((csc theta + 1)/(csc theta - 1)) + sqrt((csc theta - 1)/(csc theta + 1)) = 2 sqrt 21. i^22. i^33. i^44. i^55. i^176. i^10177. (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)^227. (2+3i)^228. 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)^439. (1- (sqrt 3)i)/(sqrt 3 + i)40. (sqrt 2)/(i^2 - i^3)41. (a+b i)(a- b i)/(1-i)^442. 2i / (3 - 3i)43. (1 + i)^344. (1 - i)^445. (7 - 7i)^246. (1+i)/i47. (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)^351. (sqrt 2)/(i^2 + i^3)52. 1/(-1 + i)^453. (a + b i)(a - b i)/(1-i)^454. i (i - 1) (sqrt 3+i)55. (1 - i) (2 - 2i) (sqrt 3+4i)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 2014. log (8, 80) - log (8, 5)15. log (10, 50) - log (10, 5)16. 2/3 log 27 + 1/3 log 817. 1/3 (2 log 8 - 6 log 3) - 2 log 2 + log 318. 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 z24. 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 x44. 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 248. log (x^2 - 1) + log y - log x49. 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 x1. 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)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))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^37. ln(e^x)/x8. 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))1. log (9, 81) = x2. log (1/2, x) = 53. log (sqrt 5, x) = -44. log sqrt (x^2 - 1) = 25. log (2x - 5) = log 86. log x + log 8 = 17. ln x = 1/2 ln x8. log(x-9) + log 100 x = 39. ln (x+1) / ln (x - 1) = 210. log (4, x+6)+ log (4, x - 6) = 311. log(6x+5) - log 3 = log 2 - log x12. log(3x+7) = 213. 2 log(x+1) = 114. ln x + ln(x+2) = 115. ln 2x + ln(3x-e) - 2 = ln 816. 2 log x - 2 = log(1-x)17. 3 log x - 3 log(x+1) = 918. log x + log (x+1) = log 1219. ln (2x+3)+ln x = ln e20. log(x^2 + 3x) = 121. log (5, x) + log (5, 2) = 222. log (2, x+1) + log (2, x+4) = 223. ln (ln x) = 024. log (log x) = 225. ln (x^3+3) = ln 4+ ln x26. log (10, x^2 - 1) - log (10, x+1) = 127. log(x^3 + 1) - 1 = log(x+1)28. (log x)^3 = log x^229. log x^2 = (log x)^230. log log x = 131. log(2x-1) + log(x-1) = 2 - log(3x+1)32. 2 log(2x-5) + log(x+7) = 133. log(5-x^2) + log(3x-5) = 034. 3 log x + log(4-3x) = 035. 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)) = -139. log(sqrt x - 2) + log(sqrt x + 2) = 140. log (10, 8) + log (10, x) + log (10, x^2) = 341. log (2, 2^(x - 1)) = 342. log (5, x^3) = 643. log(sqrt(x-1) + 1) + 2 log(sqrt(x-1)-2) = 2 log 244. log (x^log x) = 1645. 3( log(2, x))^2+log (2, x) - 2 = 046. log (x - 4) - log (3x - 10) = log (1/x)47. abs (log (4, x)) = 248. 2 log x + log a = 049. 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 x52. a = ln x + ln(2-x)53. a = 2 ln x - ln(2x-1)54. a = ln(x + sqrt(x^2 + 4))�5..4;	5f./;V	5�.Woz	5�.;˞	5�.2�	5�.>B�	5.1�	�	�V	&�	5�.3]p	5�.:��	5�.=��	�	5.7V�	5).6�	5N.5�>	�	>�	u	4:!;9!I?I!I/4:!;9!I?$>%I6.�
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