`sin[cot^(-1){tan(cos^(-1)x)}]` is e uq (a) `x` (b) `sqrt(1-x^2)` (c) `1/x` (d) None of these

Explanation

We have given

`sincot^(−1)tancos^(−1)x
∴cos^(−1)x=tan^(−1)(sqrt(1-x^2)/x)`

`⇒sincot^(−1)tantan^(−1)(sqrt(1-x^2)/x)`

`⇒sincot^(−1)(sqrt(1-x^2)/x)`

`⇒sintan^(−1)(x/(sqrt(1-x^2)))`

`⇒sinsin^(−1)x`

`⇒x`

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