Prove that:`cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx)))=x/2, x in (0,pi/4)`

Explanation

To prove that

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

we will simplify the left-hand side step by step.

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