Answer
$\frac{\sqrt{2}}{2}$
Work Step by Step
Use the first Sum-to-Product Formula, $\cos x-\cos y=-2\sin \frac{x+y}{2}\sin\frac{x-y}{2}$.
$\cos 255^\circ-\cos 195^\circ$
$=-2\sin \frac{255^\circ+195^\circ}{2}\sin \frac{255^\circ-195^\circ}{2}$
$=-2\sin \frac{450^\circ}{2}\sin\frac{60^\circ}{2}$
$=-2\sin 225^\circ\sin 30^\circ$
$=-2\times(-\frac{\sqrt{2}}{2})\times\frac{1}{2}$
$=\frac{\sqrt{2}}{2}$
