$\cot^{-1}\big(\sqrt{\cos\alpha}-\tan^{-1}(\sqrt{\cos\alpha}\big)=x$ then $\sin x=?$

Question

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