Answer
$\frac{1}{2}\sqrt{2+\sqrt{3}}$
Work Step by Step
Use the half-angle formula, $\cos\frac{u}{2}=\pm\sqrt{\frac{1+\cos u}{2}}$. Note that $15^\circ$ is in Quadrant I, where cosine is positive, so we take the positive square root.
$\cos 15^\circ$
$=\cos \frac{30^\circ}{2}$
$=\sqrt{\frac{1+\cos 30^\circ}{2}}$
$=\sqrt{\frac{1+\frac{\sqrt{3}}{2}}{2}}$
$=\sqrt{\frac{(1+\frac{\sqrt{3}}{2})*2}{2*2}}$
$=\sqrt{\frac{2+\sqrt{3}}{4}}$
$=\frac{\sqrt{2+\sqrt{3}}}{\sqrt{4}}$
$=\frac{1}{2}\sqrt{2+\sqrt{3}}$
