和積の公式2

$3$\displaystyle{2\cos \frac{\hspace{2} x+y \hspace{2}}{\hspace{2}2\hspace{2}}\sin \frac{\hspace{2} x- y \hspace{2}}{\hspace{2}2\hspace{2}}}$

$3$\displaystyle{\frac{\hspace{2}1\hspace{2}}{\hspace{2}2\hspace{2}} \{ \sin $ {\alpha}+{\beta} $ +\sin $ {\alpha}- {\beta} $ \} }$ ※

$3$\displaystyle{\begin{array}{lll}=\frac{\hspace{2}1\hspace{2}}{\hspace{2}2\hspace{2}} \{\begin{array}{lll}\sin $ \frac{\hspace{2} x- y \hspace{2}}{\hspace{2}2\hspace{2}}+\frac{\hspace{2} x+y \hspace{2}}{\hspace{2}2\hspace{2}} $ & \vspace{6}\\ +\sin $ \frac{\hspace{2} x- y \hspace{2}}{\hspace{2}2\hspace{2}}- \frac{\hspace{2} x+y \hspace{2}}{\hspace{2}2\hspace{2}} $ & \vspace{6}\\ \end{array}\} & \vspace{6}\\ =\frac{\hspace{2}1\hspace{2}}{\hspace{2}2\hspace{2}} \{ \sin x+\sin $ - y $ \} & \vspace{6}\\ =\frac{\hspace{2}1\hspace{2}}{\hspace{2}2\hspace{2}} $ \sin x- \sin y $ & \vspace{6}\\ \end{array}}$

$3$\displaystyle{2\cos \frac{\hspace{2} x+y \hspace{2}}{\hspace{2}2\hspace{2}}\sin \frac{\hspace{2} x- y \hspace{2}}{\hspace{2}2\hspace{2}}}$