Find the value of $\tan\big[\large\frac{1}{2}$$\big(\sin^{-1}\large\frac{2x}{1+x^2}+$$\cos^{-1}\large\frac{1-y^2}{1+y^2}\big)\big],$$\mid x\mid < 1,y > 0$ and $xy <1$

Question

$\begin{array}{1 1}(a)\;\large\frac{xy}{1-xy}&(b)\;\large\frac{x-y}{1-xy}\\(c)\;\large\frac{x+y}{1-xy}&(d)\;None\;of\;these\end{array}$