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Additionstheoreme

$$\begin{align}
\sin( \alpha + \beta ) &= \sin \alpha \cdot \cos \beta + \cos \alpha \cdot \sin \beta \\
\cos( \alpha + \beta ) &= \cos \alpha \cdot \cos \beta – \sin \alpha \cdot \sin \beta \\
\tan ( \alpha + \beta ) &= \frac{\tan \alpha + \tan \beta}{1 – \tan \alpha \cdot \tan \beta} \qquad \alpha + \beta \neq 90^\circ \qquad \tan \alpha \cdot \tan \beta \neq 1 \\
\sin( \alpha – \beta ) &= \sin \alpha \cdot \cos \beta – \cos \alpha \cdot \sin \beta \\
\cos( \alpha – \beta ) &= \cos \alpha \cdot \cos \beta + \sin \alpha \cdot \sin \beta \\
\tan ( \alpha – \beta ) &= \frac{\tan \alpha + \tan \beta}{1 + \tan \alpha \cdot \tan \beta} \qquad \text{s.o.} \\
\sin ( 2\alpha ) &= 2 \sin\alpha \cdot \cos \alpha \\
\cos ( 2\alpha) &= \cos^2 \alpha – \sin^2 \alpha \\
\sin(-\alpha) &= – \sin \alpha
\end{align}$$