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Need Solution for R.D.Sharma Maths Class 12 Chapter 3 Inverse Trigonomeric Functions Exercise MCQs Question 7 Maths Textbook Solution.

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Answer: x

Hint: Take \cos ^{-1} x=y

Given: \sin \left[\cot ^{-1}\left\{\tan \left(\cos ^{-1} x\right)\right\}\right]


\begin{aligned} &\text { Let } \cos ^{-1} x=y \\ &\cos y=x \end{aligned}

\begin{aligned} \sin \left[\cot ^{-1}\left\{\tan \left(\cos ^{-1} x\right)\right\}\right] &=\sin \left[\cot ^{-1}\{\tan y\}\right] \\ &=\sin \left[\cot ^{-1}\left\{\cot \left(\frac{\pi}{2}-y\right)\right\}\right] \\ &=\sin \left[\frac{\pi}{2}-y\right] \\ &=\cos y \\ &=x \end{aligned}  Mention the formula used

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