# Question #79779

Mar 8, 2016

$\sin \left(3 \theta\right) = \sin \left(2 \theta + \theta\right) = \sin 2 \theta \cos \theta + \cos 2 \theta \sin \theta$
$\cos \left(3 \theta\right) = \cos \left(2 \theta + \theta\right) = \cos \left(2 \theta\right) \cos \theta - \sin \left(2 \theta \sin \theta\right)$
$\tan \left(3 \theta\right) = \tan \left(2 \theta + \theta\right) = \frac{\tan \left(2 \theta\right) + \tan \theta}{1 - \tan \left(2 \theta\right) \left(\tan \theta\right)}$

#### Explanation:

$\sin \left(3 \theta\right) = \sin \left(2 \theta + \theta\right) = \sin 2 \theta \cos \theta + \cos 2 \theta \sin \theta$
$\cos \left(3 \theta\right) = \cos \left(2 \theta + \theta\right) = \cos \left(2 \theta\right) \cos \theta - \sin \left(2 \theta \sin \theta\right)$
$\tan \left(3 \theta\right) = \tan \left(2 \theta + \theta\right) = \frac{\tan \left(2 \theta\right) + \tan \theta}{1 - \tan \left(2 \theta\right) \left(\tan \theta\right)}$
Note you can simplify the double angles by using the appropriate double angle formula to dissolve it