Prove the following: `cot^(-1)[(sqrt(1+sinx )+sqrt(1-sinx))/(sqrt(1+sinx)-\ sqrt(1-sinx))]=x/2,\ x (0,pi/4)`

Explanation

To prove the statement

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

we will follow these steps:

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