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Question

The x satisfying sin1x+sin1(1x)=cos1x are:
  1. 1, 0
  2. 1, -1
  3. 0,12
  4. None


Solution

The correct option is C 0,12
We have, sin1(1x)=(π2sin1x)sin1x=π22sin1x
Taking sine of both sides,
1x=sin(π22sin1x)=cos(2sin1x)=cos2θ=12sin2θ, Where sin1x=θ
Or 1x=12x2 or x (1-2x)=0
x=0,12

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