## Precalculus (6th Edition) Blitzer

$2-\sqrt 3$
Using the half-angle formula $tan\frac{u}{2}=\frac{1-cos(u)}{sin(u)}$, we have $tan\frac{\pi}{12}=\frac{1-cos(\frac{\pi}{6})}{sin(\frac{\pi}{6})}=\frac{1-\sqrt 3/2}{1/2}=2-\sqrt 3$