#### Answer

$\sin^2 x-\sin^2 y=\cos^2 y-\cos^2 x$

#### Work Step by Step

Start with the left side:
$\sin^2 x-\sin^2 y$
Rewrite $\sin^2 x$ as $1-\cos^2 x$ and $\sin^2 y$ as $1-\cos^2 y$:
$=(1-\cos^2 x)-(1-\cos^2 y)$
Simplify:
$=1-\cos^2 x-1+\cos^2 y$
$=\cos^2y-\cos^2 x$
Since this equals the right side, the identity has been proven.