$\displaystyle\lim_{x \to \frac{\pi}{2}} \frac{[1- \tan(\frac{x}{2})][1 - \sin x]}{[1+\tan(\frac{x}{2})][\pi - 2x]^3}$ is :

Question

( A ) $\infty$
( B ) $\frac{1}{32}$
( C ) $0$
( D ) $\frac{1}{8}$