Somformule van de tangens

$\eqalign{ & \tan (\alpha + \beta ) = \cr & \frac{{\sin (\alpha + \beta )}} {{\cos (\alpha + \beta )}} = \cr & \frac{{\sin \alpha \cos \beta + \cos \alpha \sin \beta }} {{\cos \alpha \cos \beta - \sin \alpha \sin \beta }} = \cr & \frac{{\frac{{\sin \alpha \cos \beta }} {{\cos \alpha \cos \beta }} + \frac{{\cos \alpha \sin \beta }} {{\cos \alpha \cos \beta }}}} {{\frac{{\cos \alpha \cos \beta }} {{\cos \alpha \cos \beta }} - \frac{{\sin \alpha \sin \beta }} {{\cos \alpha \cos \beta }}}} = \cr & \frac{{\tan \alpha + \tan \beta }} {{1 - \tan \alpha \tan \beta }} \cr}$

Voorbeeld
$\tan 75^\circ  = \tan \left( {45^\circ  + 30^\circ } \right) = \sqrt 3  + 2$

Verdubbelingsformule
$\eqalign{\tan (2\alpha ) = \frac{{2\tan \alpha }} {{1 - \tan ^2 \alpha }}}$