The value of cos left(tan ^{-1}left(sin left( | vedclass

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(D) Let $	heta = \cot^{-1} x$,then $\cot 	heta = x$. Since $\cot 	heta = \frac{x}{1}$,we have $\sin 	heta = \frac{1}{\sqrt{1+x^2}}$.Thus,$\sin(\co

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$\sqrt{\frac{x^2+1}{x^2+2}}$

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(D) Let $	heta = \cot^{-1} x$,then $\cot 	heta = x$. Since $\cot 	heta = \frac{x}{1}$,we have $\sin 	heta = \frac{1}{\sqrt{1+x^2}}$.Thus,$\sin(\cot^{-1} x) = \frac{1}{\sqrt{1+x^2}}$.Now,let $\phi = 	an^{-1} \left( \frac{1}{\sqrt{1+x^2}} ight)$,then $	an \phi = \frac{1}{\sqrt{1+x^2}}$.We need to find $\cos \phi$. Using the identity $\sec^2 \phi = 1 + 	an^2 \phi$,we get $\sec^2 \phi = 1 + \frac{1}{1+x^2} = \frac{1+x^2+1}{1+x^2} = \frac{x^2+2}{x^2+1}$.Therefore,$\cos^2 \phi = \frac{x^2+1}{x^2+2}$,which implies $\cos \phi = \sqrt{\frac{x^2+1}{x^2+2}}$.

The value of $\cos \left(\tan ^{-1}\left(\sin \left(\cot ^{-1} x\right)\right)\right)$ is

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