If $\cos x=\large\frac{2\cos y-1}{2-\cos y}$ where $x,y\in (0,\pi)$ then $\tan\large\frac{x}{2}$$.\cot\large\frac{y}{2}$ is equal to

Question

$(a)\;\sqrt 2\qquad(b)\;\sqrt 3\qquad(c)\;\large\frac{1}{\sqrt 2}$$\qquad(d)\;\large\frac{1}{\sqrt 3}$