If $\large\frac{1+\sin 2x}{1-\sin 2x}$$=\cot^2(a+x)$ $\forall x\in R\sim \big(n\pi+\large\frac{\pi}{4}\big)$$ n\in N$ then $'a'$ is equal to

Question

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