Angle addition identities

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The trigonometric angle addition identities state the following identities:

$\sin(x + y) = \sin (x) \cos (y) + \cos (x) \sin (y)$ $\cos(x + y) = \cos (x) \cos (y) - \sin (x) \sin (y)$ $\tan(x + y) = \frac{\tan (x) + \tan (y)}{1 - \tan (x) \tan (y)}$

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