Evaluate $\cot^{-1} \left ( \large \frac {{\sqrt {1+\sin x}}+{\sqrt {1-\sin x}}}{{\sqrt {1+\sin x}}-{\sqrt {1-\sin x}}} \right ) = \large \frac {x}{2}$$, x \in \left ( 0, \frac{\pi}{4} \right )$

Question

$\begin{array}{1 1} 0 \\ 1 \\ \large\frac{x}{2} \\ \large\frac{-x}{2}\end{array}$