Answer
$-\frac{\sqrt3-1}{2\sqrt2}$
Work Step by Step
Using the given formula and the known values: $\sin-165^\circ=\sin-120^\circ\cos45^\circ-\sin45^\circ\cos-120^\circ=-\frac{\sqrt3}{2}\frac{1}{\sqrt2}-\frac{1}{\sqrt2}(-\frac{1}{2})=-\frac{\sqrt3-1}{2\sqrt2}$
