Answer
$ \frac{\sqrt 2-\sqrt 6}{4}$
Work Step by Step
$cos\frac{7\pi}{12}=cos(\frac{\pi}{3}+\frac{\pi}{4})
=cos\frac{\pi}{3} cos\frac{\pi}{4}-sin\frac{\pi}{3} sin\frac{\pi}{4}
=(\frac{1}{2})(\frac{\sqrt 2}{2})-(\frac{\sqrt 3}{2})(\frac{\sqrt 2}{2})
=\frac{\sqrt 2-\sqrt 6}{4}$
