Prove that: `"sin"[cot^(-1){"cos"(tan^(-1)x)}]=sqrt((x^2+1)/(x^2+2))`` ``cos"[tan^(-1){"sin"(cot^(-1)x)}]=sqrt((x^2+1)/(x^2+2))``

Explanation

A)`sin [cot ^{-1}(cos (tan ^{-1} x))]`

let `tan ^{-1} x=theta`

`tan theta={x}`



`Rightarrow cos theta=frac{1}{sqrt{1+{x}^{2}}}={a}`



the function is reduced to `sin [cot ^{-1} {a}]`

let `cot ^{-1} {a}=theta_{2}`


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