# Formelsammlung Mathematik: Identitäten: Prosthaphäretische Formeln

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### Formeln nach Werner

${\displaystyle 1.\quad \sin(\alpha +\beta )+\sin(\alpha -\beta )=2\cdot \sin \alpha \cdot \cos \beta }$

${\displaystyle 2.\quad \sin(\alpha +\beta )-\sin(\alpha -\beta )=2\cdot \cos \alpha \cdot \sin \beta }$

${\displaystyle 3.\quad \cos(\alpha +\beta )+\cos(\alpha -\beta )=2\cdot \cos \alpha \cdot \cos \beta }$

${\displaystyle 4.\quad \cos(\alpha +\beta )-\cos(\alpha -\beta )=-2\cdot \sin \alpha \cdot \sin \beta }$

### Formeln nach Simpson

${\displaystyle 1.\quad \sin \alpha +\sin \beta =2\cdot \sin {\frac {\alpha +\beta }{2}}\cdot \cos {\frac {\alpha -\beta }{2}}}$

${\displaystyle 2.\quad \sin \alpha -\sin \beta =2\cdot \cos {\frac {\alpha +\beta }{2}}\cdot \sin {\frac {\alpha -\beta }{2}}}$

${\displaystyle 3.\quad \cos \alpha +\cos \beta =2\cdot \cos {\frac {\alpha +\beta }{2}}\cdot \cos {\frac {\alpha -\beta }{2}}}$

${\displaystyle 4.\quad \cos \alpha -\cos \beta =-2\cdot \sin {\frac {\alpha +\beta }{2}}\cdot \sin {\frac {\alpha -\beta }{2}}}$