The value of sin (cot ^{-1} x) is | vedclass

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Question

(A) Let $\cot ^{-1} x = t$. Then,$x = \cot t$. We know the identity $1 + \cot^2 t = \operatorname{cosec}^2 t$. Substituting $x$,we get $1 + x^2 = \ope

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

Vedclass · Answer

(A) Let $\cot ^{-1} x = t$. Then,$x = \cot t$. We know the identity $1 + \cot^2 t = \operatorname{cosec}^2 t$. Substituting $x$,we get $1 + x^2 = \operatorname{cosec}^2 t$. Therefore,$\operatorname{cosec} t = \sqrt{1 + x^2}$. Since $\sin t = \frac{1}{\operatorname{cosec} t}$,we have $\sin t = \frac{1}{\sqrt{1 + x^2}}$. Thus,$\sin (\cot ^{-1} x) = \frac{1}{\sqrt{1 + x^2}}$.

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

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