Sum and Difference of Two Angles

Go to the derivation of sum and difference of two angles if you want information on where these formulas came from.

1. $ \sin (\alpha + \beta) = \sin \alpha \, \cos \beta + \cos \alpha \, \sin \beta $
2. $ \sin (\alpha - \beta) = \sin \alpha \, \cos \beta - \cos \alpha \, \sin \beta $
3. $ \cos (\alpha + \beta) = \cos \alpha \, \cos \beta - \sin \alpha \, \sin \beta $
4. $ \cos (\alpha - \beta) = \cos \alpha \, \cos \beta + \sin \alpha \, \sin \beta $
5. $ \tan (\alpha + \beta) = \dfrac{\tan \alpha + \tan \beta}{1 - \tan \alpha \, \tan \beta} $
6. $ \tan (\alpha - \beta) = \dfrac{\tan \alpha - \tan \beta}{1 + \tan \alpha \, \tan \beta} $
 

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