## Precalculus (6th Edition)

$2-\sqrt{3}$
Use the half-angle formula, $\tan\frac{u}{2}=\frac{1-\cos u}{\sin u}$. $\tan 195^\circ$ $=\tan \frac{390^\circ}{2}$ $=\frac{1-\cos 390^\circ}{\sin 390^\circ}$ $=\frac{1-\cos 30^\circ}{\sin 30^\circ}$ $=\frac{1-\frac{\sqrt{3}}{2}}{\frac{1}{2}}$ $=\frac{1-\frac{\sqrt{3}}{2}}{\frac{1}{2}}*\frac{2}{2}$ $=\frac{2-\sqrt{3}}{1}$ $=2-\sqrt{3}$