If $\cot^{-1}(\sqrt{\cos\alpha})-\tan^{-1}(\sqrt{\cos\alpha})=x$ then $\sin x$ is equal to

Question

$\begin{array}{1 1}(a)\;\tan^2\big(\large\frac{\alpha}{2})&(b)\;\cot^2\big(\large\frac{\alpha}{2}\big)\\(c)\;\tan\alpha&(d)\;\cot\big(\large\frac{\alpha}{2})\end{array}$