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

We have;

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

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

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

$\therefore$ Maximum value of $\cos [\cos (x)]=\cos (0)=1^{\prime}$

And, minimum value of $\cos [\cos (x)]=c \cos (1)$