Solve: `cos(sin^(-1)x)=1/6`

Explanation

`Let \sin ^{-1}x= a`

`\implies x=\sin a`

`\implies x^{2}=\sin ^{2} a`

`\implies \cos ^{2} a=1-\sin ^{2} a=1`

`\implies \cos a=\sqrt{1-x^{2}}`

`\implies a=\cos ^{-1} \sqrt{1-x^{2}}`

We have, `\cos (\sin ^{-1} x)=\frac{1}{6}`

`\implies \cos a=\frac{1}{6} \text { where } \sin ^{-1} x=a`

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