Write the maximum value of sin (cos x).

We have:

$-1 \leq \cos x \leq 1$

Also, $\sin (-\theta)=-\sin \theta$

When the angle increases from 0 to $\frac{\pi}{2}$, the value of $\sin \theta$ also increases.

$\therefore$ Maximum value of $\sin [\cos x]=\sin (1)$