prove the following : $ \cot^{-1} \bigg(\large \frac{\sqrt {1+\sin x} + \sqrt {1-\sin x}}{\sqrt {1+\sin x} - \sqrt {1-\sin x}} \bigg) = \large\frac{x}{2},$$ x \in \: \bigg(0,\large \frac{\pi}{4} \bigg) $

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