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BITSAT The value of sin(cot-1 x) is

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

Answers (1)

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A Abhishek Sahu

Let $\cot ^{-1}x = \Theta$

$\Rightarrow \cot\Theta = x$

Using Pythagoras theorem, $\sin \Theta =\frac{1}{\sqrt{1+x^2}}$

$\Rightarrow \Theta =\sin ^{-1} \left ( \frac{1}{\sqrt{1+x^2}} \right )$

$\sin \left ( \sin ^{-1} \left ( \frac{1}{\sqrt{1+x^2}} \right ) \right ) = \frac{1}{\sqrt{1+x^2}}$

Option (2) is correct

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