# 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. $\tan (\alpha - \beta) = \dfrac{\tan \alpha - \tan \beta}{1 + \tan \alpha \, \tan \beta}$