Write the maximum and minimum values of sin (sin x).

We know :

$-1 \leq \sin x \leq 1$

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 $\sin [\sin (x)]=\sin (1)$

And, minimum value of $\sin [\sin (x)]=\sin (-1)=-\sin 1$