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

Question

( A ) $\tan^2(\frac{\alpha}{2})$
( B ) $\cot (\frac{\alpha}{2})$
( C ) $\tan \alpha$
( D ) $\cot^2(\frac{\alpha}{2})$