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Question

sin1[x1xx1x2]=


  1. sin1xsin11x
     

  2. sin1x+sin11x
     

  3. sin1xsin1x
     

  4. None


Solution

The correct option is C

sin1xsin1x
 


sin1[x1xx1x2]
Substitute x=sinθ and x=sinϕ so that θ=sin1x and ϕ=sin1x
We get sin1[sinθ1sin2ϕsinϕ1sin2θ]
=sin1[sinθcosϕsinϕcosθ]=sin1[sin(θϕ)]=θϕ=sin1xsin1x

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