Answer
$ \frac{\sqrt {2+\sqrt 3}}{2}$ or
$\frac{\sqrt 6+\sqrt 2}{4}$
Work Step by Step
$cos15^\circ=cos\frac{30^\circ}{2}=\sqrt {\frac{1+cos30^\circ}{2}}
=\sqrt {\frac{1+\sqrt 3/2}{2}}=\frac{\sqrt {2+\sqrt 3}}{2}$
Note: this is the same as $\frac{\sqrt 6+\sqrt 2}{4}$