Answer
$\frac{\sqrt 6-\sqrt 2}{4}$
Work Step by Step
Using trigonometric identities, we have
$sin15^\circ=sin(45^\circ-30^\circ)=sin45^\circ cos30^\circ-cos45^\circ sin30^\circ=(\frac{\sqrt 2}{2})(\frac{\sqrt 3}{2})-(\frac{\sqrt 2}{2})(\frac{1}{2})=\frac{\sqrt 6-\sqrt 2}{4}$
