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Question

sin1[x1xx1x2]=


A

sin1xsin11x

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B

sin1x+sin11x

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C

sin1xsin1x

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D

None

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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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