Prove that : \[ \cot ^{-1}\left(\frac{\sqrt{1+\sin x}+\sqrt{1-\sin ...

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Prove that :
\[
\cot ^{-1}\left(\frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}\right)=\frac{x}{2} ; x \in\left(0, \frac{\pi}{4}\right)
\]
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