sin α cos β = 1 2 { sin ( α + β ) + sin ( α − β ) } {\displaystyle \sin \alpha \cos \beta ={\frac {1}{2}}\left\{\sin(\alpha +\beta )+\sin(\alpha -\beta )\right\}}
cos α sin β = 1 2 { sin ( α + β ) − sin ( α − β ) } {\displaystyle \cos \alpha \sin \beta ={\frac {1}{2}}\left\{\sin(\alpha +\beta )-\sin(\alpha -\beta )\right\}}
cos α cos β = 1 2 { cos ( α + β ) + cos ( α − β ) } {\displaystyle \cos \alpha \cos \beta ={\frac {1}{2}}\left\{\cos(\alpha +\beta )+\cos(\alpha -\beta )\right\}}
sin α sin β = − 1 2 { cos ( α + β ) − cos ( α − β ) } {\displaystyle \sin \alpha \sin \beta =-{\frac {1}{2}}\left\{\cos(\alpha +\beta )-\cos(\alpha -\beta )\right\}}
sin A + sin B = 2 sin A + B 2 cos A − B 2 {\displaystyle \sin A+\sin B=2\sin {\frac {A+B}{2}}\cos {\frac {A-B}{2}}}
sin A − sin B = 2 cos A + B 2 sin A − B 2 {\displaystyle \sin {A}-\sin {B}={2}\cos {\frac {A+B}{2}}\sin {\frac {A-B}{2}}}
cos A + cos B = 2 cos A + B 2 cos A − B 2 {\displaystyle \cos {A}+\cos {B}={2}\cos {\frac {A+B}{2}}\cos {\frac {A-B}{2}}}
cos A − cos B = − 2 sin A + B 2 sin A − B 2 {\displaystyle \cos A-\cos B=-2\sin {\frac {A+B}{2}}\sin {\frac {A-B}{2}}}
