13. Find all real numbers $a$ and $b$ so that for all real numbers $x$,
$$
2 \cos ^{2}\left(x+\frac{b}{2}\right)-2 \sin \left(a x-\frac{\pi}{2}\right) \cos \left(a x-\frac{\pi}{2}\right)=1
$$
13. $a=1$ and $b=-\frac{3 \pi}{2}+2 k \pi$, or $a=-1$ and $b=\frac{3 \pi}{2}+2 k \pi$ where $k \in \mathbb{Z}$