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