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Question

How do you simplify cos(sin1x) ?

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Solution

±1x2
Explanation:
cos(sin1x)
Let,
sin1x=θ
sinθ=x
sin2θ=x2
1cos2θ=x2
cos2θ=1x2
cosθ=±1x2
θ=cos1±1x2
Putting this,
cos(cos1±1x2)
=±1x2
But sin1x is, definition, in [π2,π2] so cos(sin1x)0
so cos(sin1x)=1x2

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