倍角、３倍角、半角の公式【三角関数】

\[ \begin{eqnarray*}\sin 2\theta&=&2\sin \theta\cos \theta \\ \cos2\theta&=&\cos^2\theta-\sin^2\theta = 1-2\sin^2 \theta = 2\cos^2\theta-1 \\ \tan 2\theta &=& \frac{2\tan \theta}{1-\tan^2\theta} \end{eqnarray*}\]

\[ \begin{eqnarray*}\sin3\theta&=&3\sin \theta-4\sin^3 \theta \\ \cos3\theta&=&4\cos^3\theta-3\cos \theta\\ \tan 3\theta &=& \frac{3\tan \theta-\tan^3\theta}{1-3\tan^2\theta} \end{eqnarray*}\]

\[ \begin{eqnarray*}\sin^2 \frac{\theta}{2}&=&\frac{1-\cos \theta}{2}\\ \cos^2 \frac{\theta}{2}&=&\frac{1+\cos \theta}{2}\\ \tan^2 \frac{\theta}{2}&=&\frac{1-\cos \theta}{1+\cos \theta}\end{eqnarray*}\]