If 'x' takes negative permissible value, then sin-1(x) is equal t

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 Multiple Choice QuestionsMultiple Choice Questions

121.

The value of sin2cos-153 is

  • 53

  • 253

  • 459

  • 259


122.

sin2sin-16365 is equal to

  • 212665

  • 46565

  • 86365

  • 6365


123.

cot-12 . 12 + cot-12 . 22 + cot-12 . 32 + ... upto  is equal to

  • π4

  • π3

  • π2

  • π5


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124.

If 'x' takes negative permissible value, then sin-1(x) is equal to

  • - cos-11 - x2

  • cos-1x2 - 1

     

  • π - cos-11 - x2

  • cos-11 - x2


A.

- cos-11 - x2

Let sin-1x = y. Then, x = sinySince,       - 1  x < 0, therefore - π2  sin-1x < 0          - π2  y < 0Now, cosy = 1 - sin2y    cosy = 1 - x2 for 0  y  πBut, - π2 y < 0 cos- y = 1 - x2        - y = cos-11 - x2            y = - cos-11 - x2


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125.

If a > b > 0, sec-1a + ba - b = 2sin-1x, then x is

  • - ba +b

  •  ba +b

  • -  aa +b

  • aa +b


126.

If x  , x  2n + 1π2, n  Z, then sin-1cosx + cos-1sinxtan-1cotx + cot-1tanx is

  • π2

  • π6

  • π4

  • π3


127.

In ABC, if a = 2, B = tan-112 and C = tan-113, then (A, b) equals

  • 3π4, 25

  • π4, 225

  • 3π4, 225

  • π4, 25


128.

The domain of f(x) = sin-1log2x2 is

  • 0  x  1

  • 0  x  4

  • 1  x  4

  • 4  x  6


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129.

If tan-1x = π4 - tan-113, then x is

  • 13

  • 12

  • 14

  • 16


130.

If cos-1yb = nlogxn, then

  • xy1 = nb2 - y2

  • xy1 + nb2 - y2 = 0

  • y1 = xb2 - y2

  • xy1 - b2 - y2 = 0


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