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The value of $\sin ({Cot}^{- 1} (\cos ({Tan}^{- 1} x)))$ is

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

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

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

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

answer is B.

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Detailed Solution

${Tan}^{- 1} x = \cos^{- 1} (\frac{1}{\sqrt{1 + x^{2}}}) n o w \sin ({Cot}^{- 1} (\cos ({Tan}^{- 1} x))) = \sin [\cot^{- 1} \frac{1}{\sqrt{1 + x^{2}}}] = \sqrt{\frac{x^{2} + 1}{x^{2} + 2}}$

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