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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

Back up to Trigonometry

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