3倍角の公式( $3$\displaystyle{\cos 3{\alpha}}$ 編)

$3$\displaystyle{\begin{array}{lll}\cos 3{\alpha}=\cos $ {\alpha}+2{\alpha} $ & \vspace{6}\\ & \vspace{6}\\ \text{\hspace{5}}=\cos {\alpha}\cos 2{\alpha}-\sin {\alpha}\sin 2{\alpha}& \vspace{6}\\ \end{array}}$
　　　　　　 (加法定理を参照)

$3$\displaystyle{\begin{array}{lll}\text{\hspace{5}}=\cos {\alpha} $ 2{ \cos }^{2}{\alpha}- 1 $ - & \vspace{6}\\ \text{\hspace{5}}\text{\hspace{5}}\text{\hspace{5}}\text{\hspace{5}}\text{\text{\hspace{5}}\text{\hspace{5}}\text{\hspace{5}}\text{\text{\hspace{5}}\text{\hspace{5}}\text{\hspace{5}}\text{\text{\hspace{5}}\text{\hspace{5}}\text{\hspace{5}}\text{\text{\hspace{5}}\text{\hspace{5}}\text{\hspace{5}}\text{\hspace{5}}\sin {\alpha}\cdot 2\sin {\alpha}\cos {\alpha}}}}}& \vspace{6}\\ \end{array}}$
　　　　　(2倍角の公式を参照)

$3$\displaystyle{\begin{array}{lll}\text{\hspace{5}}=\cos {\alpha} $ 2{ \cos }^{2}{\alpha}- 1 $ - & \vspace{6}\\ \text{\hspace{5}}\text{\hspace{5}}\text{\hspace{5}}\text{\hspace{5}}\text{\hspace{5}}\text{\hspace{5}}\text{\hspace{5}}\text{\hspace{5}}\text{\hspace{5}}\text{\hspace{5}}\text{\hspace{5}}\text{\hspace{5}}\text{\hspace{5}}\text{\hspace{5}}2 $ 1- { \cos }^{2}{\alpha} $ \cos {\alpha}& \vspace{6}\\ \end{array}}$

$3$\displaystyle{\text{\hspace{5}}=4{\cos }^{3}{\alpha}- 3\cos {\alpha}}$

<参照>
加法定理
2倍角の公式

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