倍角公式

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屬性

$\begin{align} & \sin 2\theta =2\sin \theta \cos \theta \\ & \cos 2\theta =\cos ^{2}\theta -\sin ^{2}\theta =2\cos ^{2}\theta -1=1-2\sin ^{2}\theta \\ \end{align}$

公式：
- 證明：
- $\begin{align} & \sin 3\theta =\sin \left( 2\theta +\theta \right)=\sin 2\theta \cos \theta +\cos 2\theta \sin \theta \\ & =2\sin \theta \cos \theta \cos \theta +\left( 1-2\sin ^{2}\theta \right)\sin \theta \\ & =2\sin \theta \left( 1-\sin ^{2}\theta \right)+\left( 1-2\sin ^{2}\theta \right)\sin \theta \\ & =2\sin \theta -2\sin ^{3}\theta +\sin \theta -2\sin ^{3}\theta \\ & =3\sin \theta -4\sin ^{3}\theta \\ \end{align}$
公式： $\cos 3\theta =4\cos ^{3}\theta -3\cos \theta \,$