三角関数の加法定理の派生公式

２倍角公式

\(\sin{2\alpha}=2\sin{\alpha}\cos{\alpha}\)
\(\cos{2\alpha}={\cos}^{2}{\alpha}-{\sin}^{2}{\alpha }\)
\(\tan{2\alpha}=\frac{2\tan{\alpha}}{1-{\tan}^{2}{\alpha}}\)

３倍角公式

\(\sin{3\alpha}=3\sin{\alpha}-4{\sin}^{3}{\alpha}\)
\(\cos{3\alpha}=4{\cos}^{3}{\alpha}-3\cos{\alpha }\)
\(\tan{3\alpha}=\frac{3\tan{\alpha}-{\tan}^{3}\alpha}{1-3{\tan}^{2}{\alpha}}\)

半角公式

\({\sin}^{2}\frac{\alpha}{2}=\frac{1-\cos{\alpha}}{2}\)
\({\cos}^{2}\frac{\alpha}{2}=\frac{1+\cos{\alpha}}{2}\)
\({\tan}^{2}\frac{\alpha}{2}=\frac{1-\cos{\alpha}}{1+\cos{\alpha}}\)