$= \mathop {\lim \limits_{x \to 0} \frac{sin(\frac{\pi}2-\frac{\pi}2.cosx)}{sin^2(\frac{x}2)}}$$= \mathop {\lim \limits_{x \to 0} \frac{sin(\frac{\pi}2(1-cosx))}{sin^2(\frac{x}2)}}$
$= \mathop {\lim \limits_{x \to 0} \frac{sin(\frac{\pi}2(2.sin^2(\frac{\pi}2))}{sin^2(\frac{x}2)}}$
$=\mathop {\lim }\limits_{x \to 0} \frac{sin(\pi.sin^2(\frac{x}2))}{sin^2(\frac{x}2)}$
$=\mathop {\lim }\limits_{x \to 0} \frac{sin(\pi.sin^2(\frac{x}2))}{\pi.sin^2(\frac{x}2)}.\pi=\pi$
(vì $\mathop {\lim }\limits_{x \to 0} \frac{sinax}{ax}=1$)