## Double Angle Identities

The double angle formulae are rarely used directly for calculating results. It’s much more common for them to be used as a tool to help with simplifying equations.

$\sin 2\theta = 2 \sin \theta \cos \theta$

$\cos 2\theta = \cos^2\theta - \sin^2\theta$

$\tan 2\theta =$ $\frac{2 \tan \theta} {1 - \tan^2\theta}$

There are lots of different (and very useful) forms to them as well. Here’s some more:

$\sin 2\theta =$ $\frac{2 \tan \theta} {1 + \tan^2\theta}$

$\cos 2\theta =$ $\frac{1 - \tan^2 \theta} {1 + \tan^2\theta}$

$\cos 2\theta = 2 \cos^2 \theta - 1$

$\cos 2\theta = 1 - 2 \sin^2 \theta$

For these plus a list of triple and half angle identities, check out Wikipedia’s page

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