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INVERSE TRIGONOMETRIC FUNCTIONS, 1., , 2., , 3., , 4., ,  3, The principal value of cos1 , is,  2 , , , , 5, 6, , (a), , , 6, , (b), , (c), , 7, 6, , (d) none of these, , The principal value of cosec–1 (2) is, (a), , , 3, , (b), , , 6, , (c), , 2, 3, , (d), , 5, 6, ,  1 , The principal value of sin1 ,  is,  2, (a), , , 4, , (b), , , 4, , (c), , 3, 4, , (d), , 5, 4, , 5, 6, ,  1, The principal value of sin1   is,  2, (a), , , 6, , (b), , (c), , 7, 6, , (d) none of these

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5., , 6., , 7., , 8., ,  1 , The principal value of cos1   is,  2, (a), , , 3, , (b), , 2, 3, , (c), , 4, 3, , (d), , , 3, , , , , , The principal value of tan1  3 is, , (a), , 2, 3, , (b), , 4, 3, , (c), , , 3, , (d) none of these, , The principal value of cos–1 (–1) is, (a), , , 4, , (b), , , 4, , (c), , 5, 4, , (d), , 3, 4, ,  2 , The principal value of sec 1 ,  is,  3, (a), , , 6, , (b), , , 6, , (c), , 5, 6, , (d), , 7, 6

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9., , 10., , 11., , 12., , , , , , The principal value of cos ec 1  2 is, , 3, 4, , (a), , , 4, , (b), , (c), , 5, 4, , (d) none of these, , , , , , The principal value of cot 1  3 is, , (a), , , 6, , (b), , , 6, , (c), , 7, 6, , (d), , 5, 6, , 5, 3, , 2 , , The value of sin1  sin  is, 3 , , (a), , 2, 3, , (b), , (c), , , 3, , (d) none of these, , 13 , , The value of cos1  cos, is, 6 , , (a), , 13, 6, , (b), , 7, 6, , (c), , 5, 6, , (d), , , 6

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13., , 14., , 15., , 16., , 7 , , The value of tan1  tan  is, 6 , , (a), , 7, 6, , (b), , 5, 6, , (c), , , 6, , (d) none of these, , 5 , , The value of cos1  cos  is, 4 , , (a), , , 4, , (b), , , 4, , (c), , 3, 4, , (d) none of these, , 8 , , The value of sec 1  sec, is, 5 , , (a), , 2, 5, , (b), , 3, 5, , (c), , 8, 5, , (d) none of these, , 4 , , The value of cos ec 1  cos ec, is, 3 , , (a), , , 3, , (b), , , 3, , (c), , 2, 3, , (d) none of these

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17., , 18., , 3 , , The value of tan1  tan  is, 4 , , (a), , 3, 4, , (b), , (c), , , 4, , (d) none of these, , ,  1 ,  sin1   = ?, 3,  2, (a) 0, , (c), , 19., , 20., , , 4, , , 2, , (b), , 2, 3, , (d) , , 1, 1, , The value of sin  sin1  cos1  = ?, 2, 2, , (a) 0, , (b) 1, , (c) –1, , (d) none of these, , If x  0 then cos (tan–1 x + cos–1x) = ?, (a) –1, , (b) 1, , (c) 0, , (d) none of these

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21., , 22., , 23., , 24., , 3, , The value of sin  cos1  is, 5, , (a), , 2, 5, , (b), , 4, 5, , (c), , 2, 5, , (d) none of these, , 2 , 2 , , , cos1  cos   sin1  sin  = ?, 3 , 3 , , , (a), , 4, 3, , (b), , (c), , 3, 4, , (d) , , tan1, ,  3   sec, , 1, , , 2, ,  2 = ?, , (a), , , 3, , (b), , (c), , 5, 3, , (d) none of these, , cos1, , (a), , , 3, , 1, 1,  2sin1 = ?, 2, 2, , 2, 3, , (c) 2, , (b), , 3, 2, , (d) none of these

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25., ,  1 ,  1 , tan1 1  cos1    sin1   = ?,  2, 2, (a) , , (c), , 26., , 27., , 2, 4, , (d), , , 2, , 1 , , tan 2 tan1   = ?, 5 4, , (a), , 7, 17, , (b), , 7, 17, , (c), , 7, 12, , (d), , 7, 12, , 1, 5, tan  cos 1, = ?, 2 , 3 , , (a), , (c), , 28., , 3, 4, , (b), , 3  5 , 2, , 5  3 , 2, , (b), , (d), , 3  5 , 2, , 5  3 , 2, , 3, , sin  cos1  = ?, 5, , (a), , 3, 4, , (b), , (c), , 3, 5, , (d) none of these, , 4, 5

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29., , 30., , 3, , cos  tan1  = ?, 4, , (a), , 3, 5, , (b), , (c), , 4, 9, , (d) none of these, , ,  1  , sin   sin1    = ?,  2 , 3, (a) 1, (c), , 31., , 32., , 4, 5, , (b) 0, , 1, 2, , (d) none of these, , 4, 1, sin  cos1  = ?, 5, 2, (a), , 1, 5, , (b), , 2, 5, , (c), , 1, 10, , (d), , 2, 10, , , 1 , , tan1 2cos  2sin1   = ?, 2 , , , (a), , , 3, , (b), , , 4, , (c), , 3, 4, , (d), , 2, 3

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33., , 34., , 35., , 36., ,  1, If cos1    x then sin x = ?, 5, (a), , 1, 26, , (b), , 5, 26, , (c), , 1, 24, , (d) none of these, ,  3,  1 , sin 1    2cos1 , =?,  2 ,  2, , , , (a), , , 2, , (b) , , (c), , 3, 2, , (d) none of these, ,  1 , tan1  1  cos1 , = ?, 2, , , (a), , , 2, , (b) , , (c), , 3, 2, , (d), , 2, 3, , (a) 1, , (b), , 1, 2, , (c) 0, , (d) none of these, , , , , , cot tan1 x  cot 1 x = ?

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37., , tan–1 1 + tan–1, , (a) tan1, , 1, =?, 3, , 4, 3, , (c) tan–12, , 38., , 39., , 40., , tan1, , (b) tan1, , 2, 3, , (d) tan–13, , 1, 1,  tan1 = ?, 2, 3, , (a), , , 3, , (b), , , 4, , (c), , , 2, , (d), , 2, 3, , 1, 2 tan–1 = ?, 3, (a) tan1, , 3, 2, , (b) tan1, , 3, 4, , (c) tan1, , 4, 3, , (d) none of these, , 1, , cos  2 tan1  = ?, 2, , (a), , 3, 5, , (b), , 4, 5, , (c), , 7, 8, , (d) none of these

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41., , 42., , 43., , 44., , 5, , sin 2 tan1 , 8, , (a), , 25, 64, , (b), , 80, 89, , (c), , 75, 128, , (d) none of these, , 4, , sin 2sin1 , 5, , (a), , 12, 25, , (b), , (c), , 24, 25, , (d) none of these, , If tan–1 x =, , 16, 25, , , 1,  tan1 then x = ?, 4, 3, , (a), , 1, 2, , (b), , (c), , 1, 6, , (d) none of these, , If tan–1 (1 + x) + tan–1 (1 – x) =, , 1, 4, , , then x = ?, 2, , (a) 1, , (b) –1, , (c) 0, , (d), , 1, 2

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45., , If sin–1 x + sin–1y =, , , 6, , (b), , , 3, , (c) , , (d), , 2, 3, , , 4, , (a), , 46., , 47., , 2, then (cos–1 x + cos–1 y) = ?, 3, , (tan–1 2 + tan–1 3) = ?, (a), , , 4, , (b), , (c), , 3, 4, , (d) , , If tan–1 x + tan–1 3 = tan–1 8 then x = ?, (a), , 1, 3, , (b), , (c) 3, , 48., , If tan–1 3x + tan–1 2x =, , 1, 5, , (d) 5, , , then x = ?, 4, , (a), , 1, or – 2, 2, , (b), , 1, or –3, 3, , (c), , 1, or –2, 4, , (d), , 1, or –1, 6

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49., , 50., , 51., , 52., , 4, 2, , tan cos1  tan1  = ?, 5, 3, , (a), , 13, 6, , (b), , 17, 6, , (c), , 19, 6, , (d), , 23, 6, , cot 1 9  cos ec 1, , 41, =?, 4, , (a), , , 6, , (b), , , 4, , (c), , , 3, , (d), , 3, 4, , Range of sin–1 x is, ,  , (a) 0, ,  2, , (b) [0, ], ,    , (c)  , ,  2 2, , (d) none of these, , Range of cos–1 x is, (a) [0, ], ,  , (b) 0, ,  2, ,    , (c)  , ,  2 2, , (d) none of these

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53., , 54., , 55., , 56., , 57., , Range of tan–1 x is, ,  , (a)  0, ,  2, ,    , (b)  , ,  2 2, ,    , (c)  , ,  2 2, , (d) none of these, , Range of sec–1 x is, ,  , (a) 0, ,  2, , (b) [0, ], ,  , (c) [0, ]   , 2, , (d) none of these, , Rang3 of cosec–1x is, ,    , (a)  , ,  2 2, ,    , (b)  , ,  2 2, ,    , (c)  ,   {0},  2 2, , (d) none of these, , Domain of cos–1 x is, (a) [0,1], , (b) [–1, 1], , (c) [–1, 0], , (d) none of these, , Domain of sec–1 x is, (a) [–1, 1], , (b) R – {0}, , (c) R – [–1, 1], , (d) R – {–1, 1}

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58., , 59., ,  1 x2  1 x 2, If tan,  1 x2  1 x2, , 1 , , (a) sin2, , (b) sin, , (c) cos2, , (d) cos , , 1, 4 , , The value of tan cos 1,  sin1,  is, 5 2, 17 , , , 29, 3, , (a), , (c), , 60., , 61., , ,    , then x2 =, , , , 3, 29, , , , (b), , 29, 3, , (d), , 3, 29, , , , 2 tan1 cos ec (tan1 x )  tan(cot 1 x is equal to, 1, x, , (a) cot–1x, , (d) cot 1, , (c) tan–1x, , (d) none of these, , If sin1 x  cos1 x , , (a), , 1, 2, , (c) , , , , then x =, 6, (b), , 1, 2, , 3, 2, , (d) none of these

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62., ,  , , (a) x, (c), , 63., , 64., , (b), , 1, x, , 1 x 2, , (d) none of these, , The number of solutions of the equation tan1 2 x  tan1 3 x , (a) 2, , (b) 3, , (c) 1, , (d) none of these, , 5 , 2 , , , If   tan 1 tan  and   tan1   tan  , then, 4 , 3 , , , (a) 4  3, (c)    , , 65., , , , sin cot  1 tan cos1 x  is equal to, , , , 7, 12, , (b) 3  , (d) none of these, , The number of real solutions of the equation, , 1  cos 2x  2 sin1(sin x ),   x   is, (a) 0, , (b) 1, , (c) 2, , (d) infinite, , , is, 4

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66., , If x < 0, y < 0 such that xy = 1, then tan–1x + tan–1y equals, (a), , , 2, , (b) , , (c) , , 67., , 68., , 69., , , 2, , (d) none of these, ,  3x ,  2x  y , If   tan1 ,  ,   tan 1,  , then    , 2, y, , x, 3, y, , , , , (a), , , 6, , (b), , (c), , , 2, , (d) , , Let f ( x )  ecos, , 1, , {sin( x  /3)}, , , 3, , 3, , . Then, f (8 / 9) , , (a) e5  /18, , (b) e13  /18, , (c) e 2  /18, , (d) none of these, , tan1, , 1, 2,  tan1, is equal to, 11, 11, , (a) 0, , (b) 1/2, , (c) –1, , (d) 1

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70., , If tan1 3  tan1 x  tan1 8, then x =, (a) 5, , (c), , 71., , 72., , 5, 14, , (b), , 1, 5, , (d), , 14, 5, , 33 , , The value of sin1  cos, is, 5 , , (a), , 3, 5, , (b) , , (c), , , 10, , (d), , , 10, , 7, 5, , 5 , 5 , , , The value cos1  cos   sin1  sin  is, 2 , 3 , , , (a), , , 2, , (b), , (c), , 10, 3, , (d) 0, , 5, 3

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73., , 74., , 75., , 76., , ,  3  , sin 2cos1    is equal to,  5 , , (a), , 6, 25, , (b), , 24, 25, , (c), , 4, 5, , (d) , , 24, 25, , If   sin1{sin( 600)}, then one of the possible values of  is, , , 2, , (a), , , 3, , (b), , (c), , 2, 3, , (d) , , 2, 3, , 2, 2x ,  2x  , 1  1  x , If 3 sin , , 4cos, , 2, tan, , 1,  is equal to, , , , , 2,  1 x2 , 3, 1, , x,  1 x2 , , , , , 1 , , (a), , 1, 3, , (b) , , (c), , 3, , (d) , , 1, 3, 3, 4, , If 4 cos1 x  sin1 x  , then the value of x is, (a), , (c), , 3, 2, 3, 2, , (b), , (d), , 1, 2, 2, 3

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77., , 78., , If tan1, (a) 0, , (b) –2, , (c) 1, , (d) 2, , If sin1 x  cos1 x   / 6 then x =, (a), , 1, 2, , (c) , , 79., , 80., , x 1, x 1,  tan1,  tan1( 7), then the value of x is, x 1, x, , 1, 2, , (b), , 3, 2, , (d) , , 3, 2, , 1, 63 , The value of sin  sin1,  is, 4, 8, , , (a), , 1, 2, , (b), , 1, 3, , (c), , 1, 2 2, , (d), , 1, 3 3, , , , cot   2cot 1 3  , 4, , (a) 7, , (b) 6, , (c) 5, , (d) none of these

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81., , If tan1(cot )  2, then  , , , 4, , (a) , , , 3, , (b) , , (c) , , , 6, , (d) none of these

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ANSWERS, 1., , (a), , 2., , (b), , 3., , (c), , 4., , (a), , 5., , (b), , 6., , (c), , 7., , (d), , 8, , (c), , 9., , (a), , 10. (d), , 11. (c), , 12. (d), , 13. (c), , 14. (a), , 15. (a), , 16. (b), , 17. (c), , 18. (c), , 19. (b), , 20. (c), , 21. (b), , 22. (d), , 23. (b), , 24. (a), , 25. (c), , 26. (b), , 27. (a), , 28. (b), , 29. (b), , 30. (a), , 31. (c), , 32. (b), , 33. (b), , 34. (c), , 35. (a), , 36. (c), , 37. (c), , 38. (b), , 39. (b), , 40. (a), , 41. (b), , 42. (c), , 43. (a), , 44. (c), , 45. (b), , 46. (c), , 47. (b), , 48. (d), , 49. (b), , 50. (b), , 51. (c), , 52. (a), , 53. (b), , 54. (c), , 55. (c), , 56. (b), , 57. (c), , 58. (a), , 59. (d), , 60. (c), , 61. (b), , 62. (a), , 63. (a), , 64. (a), , 65. (c), , 66. (b), , 67. (a), , 68. (b), , 69. (d), , 70. (b), , 71. (d), , 72. (d), , 73. (d), , 74. (a), , 75. (a), , 76. (c), , 77. (d), , 78. (b), , 79. (c), , 80. (a), , 81. (c)