Answer
$x=\frac{\pi}{4}$ or $\frac{5\pi}{4}$, $y=\frac{\pi}{2}$
Work Step by Step
From the equation, we have
$\cos x=\sin x$ and $\sin y=1$.
$\cos x=\sin x$ implies $\tan x=1$.
$\tan x=1$ when $x=\frac{\pi}{4}$ or $\frac{5\pi}{4}$.
$\sin y=1=\sin \frac{\pi}{2}$. That is, $y=\frac{\pi}{2}$.
