sinαcosβ=12{sin(α+β)+sin(α−β)}{\displaystyle \sin \alpha \cos \beta ={\frac {1}{2}}\left\{\sin(\alpha +\beta )+\sin(\alpha -\beta )\right\}}
cosαsinβ=12{sin(α+β)−sin(α−β)}{\displaystyle \cos \alpha \sin \beta ={\frac {1}{2}}\left\{\sin(\alpha +\beta )-\sin(\alpha -\beta )\right\}}
cosαcosβ=12{cos(α+β)+cos(α−β)}{\displaystyle \cos \alpha \cos \beta ={\frac {1}{2}}\left\{\cos(\alpha +\beta )+\cos(\alpha -\beta )\right\}}
sinαsinβ=−12{cos(α+β)−cos(α−β)}{\displaystyle \sin \alpha \sin \beta =-{\frac {1}{2}}\left\{\cos(\alpha +\beta )-\cos(\alpha -\beta )\right\}}
sinA+sinB=2sinA+B2cosA−B2{\displaystyle \sin A+\sin B=2\sin {\frac {A+B}{2}}\cos {\frac {A-B}{2}}}
sinA−sinB=2cosA+B2sinA−B2{\displaystyle \sin {A}-\sin {B}={2}\cos {\frac {A+B}{2}}\sin {\frac {A-B}{2}}}
cosA+cosB=2cosA+B2cosA−B2{\displaystyle \cos {A}+\cos {B}={2}\cos {\frac {A+B}{2}}\cos {\frac {A-B}{2}}}
cosA−cosB=−2sinA+B2sinA−B2{\displaystyle \cos A-\cos B=-2\sin {\frac {A+B}{2}}\sin {\frac {A-B}{2}}}