If $x\in(\pi,2\pi)$ and $\large\frac{\sqrt{1+\cos x}+\sqrt{1-\cos x}}{\sqrt{1+\cos x}-\sqrt{1-\cos x}}$$=\cot\big(a+\large\frac{x}{2}\big)$ then $'a'$ is equal to

Question

$(a)\large\frac{\pi}{4}$$\qquad(b)\;\large\frac{\pi}{2}$$\qquad(c)\;\large\frac{\pi}{3}$$\qquad(d)\;None\;of\;these$