Simplify $\tan^{-1}\big(\large \frac{\cos x}{1+\sin x}\big)$

Question

$\begin{array}{1 1} \large \frac{\pi}{4}-\frac{x}{2} \\ \large \frac{\pi}{4}+\frac{x}{2} \\ \large \frac{\pi}{4}-\frac{x}{4} \\ \large \frac{\pi}{4}+\frac{x}{4} \end{array} $