Answer
$-\frac{1+\sqrt3}{2\sqrt2}$
Work Step by Step
Using the given formula and the known values: $\sin255^\circ=\sin210^\circ\cos45^\circ+\sin45^\circ\cos210^\circ=\frac{1}{2}\frac{1}{\sqrt2}+\frac{1}{\sqrt2}(-\frac{\sqrt3}{2})=-\frac{1+\sqrt3}{2\sqrt2}$
