Answer
$-\frac{1+\sqrt3}{2\sqrt2}$
Work Step by Step
Using the given formula and the known values: $\sin(-\frac{7\pi}{12})=\sin(-\pi/3)\cos(-\pi/4)+\cos(-\pi/3)\sin(-\pi/4)=-\frac{\sqrt3}{2}\frac{1}{\sqrt2}+\frac{1}{2}(-\frac{1}{\sqrt2})=-\frac{1+\sqrt3}{2\sqrt2}$
