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Addition Theorems for Sine and Cosine

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For the trigonometric functions $ \sin(x)$ and $ \cos(x)$ the following relations holds:

  1. $ \cos(\alpha+\beta) = \cos\alpha\cos\beta - \sin\alpha\sin\beta$
  2. $ \sin(\alpha+\beta) = \sin\alpha\cos\beta + \sin\beta\cos\alpha$

Especially:

$\displaystyle \cos (2\alpha)=\cos^2 \alpha-\sin^2 \alpha, \qquad \sin (2\alpha)=2\sin \alpha \cos \alpha$

Example:

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  automatically generated 4/ 7/2008