The value of \( \cot ^{-1}\left[\frac{\sqrt{1+\sin x}+\sqrt{1-\sin ...

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The value of \( \cot ^{-1}\left[\frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}\right] \) is
\( \mathrm{P} \)
equal to \( \left[x \in\left(0, \frac{\pi}{4}\right)\right] \)
(1) \( \frac{x}{2} \)
(2) \( \frac{-x}{2} \)
(3) \( \pi-\frac{x}{2} \)
(4) \( \frac{\pi}{4}+\frac{x}{2} \)
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