The period of $f(x)=\frac{1}{2}[\cos (\sin x)+\cos (\cos x)]$ is :

$\pi$ $\pi / 2$ $\pi / 4$ $2 \pi$

$\pi / 2$

$f(x+\pi / 2)=\frac{1}{2}[\cos (\sin (x+\pi / 2))+\cos (\cos (x+\pi / 2))]$ $=\frac{1}{2}[\cos (\cos x)+\cos (\sin x)]$ period = $\pi / 2$