The function
^2+(\;\sin (\sin x)\^2" alt="f(x)= (\;\cos (\cos x)\^2+(\;\sin (\sin x)\^2" />
is even and periodic with period so, we only need to find the maximum on .
The values of at the endpoints of are:
Prove that there are no singular points in so, the absolute maximun of is and the absolute minimum .