Answer
$2-\sqrt{3}$
Work Step by Step
Use the half-angle formula, $\tan\frac{u}{2}=\frac{1-\cos u}{\sin u}$.
$\tan 15^\circ$
$=\tan \frac{30^\circ}{2}$
$=\frac{1-\cos 30^\circ}{\sin 30^\circ}$
$=\frac{1-\frac{\sqrt{3}}{2}}{\frac{1}{2}}$
$=\frac{(1-\frac{\sqrt{3}}{2})*2}{\frac{1}{2}*2}$
$=\frac{2-\sqrt{3}}{1}$
$=2-\sqrt{3}$
