# Sum and Difference Formulas

## Sum and Difference Formula for Cosine

Given two angles ${\displaystyle \alpha {\text{ and }}\beta }$ we have the following formulas:

${\displaystyle \cos(\alpha +\beta )=\cos(\alpha )\cos(\beta )-\sin(\alpha )\sin(\beta )}$
${\displaystyle \cos(\alpha -\beta )=\cos(\alpha )\cos(\beta )+\sin(\alpha )\sin(\beta )}$

## Sum and Difference Formula for Sine

Given two angles ${\displaystyle \alpha {\text{ and }}\beta }$ we have the following formulas:

${\displaystyle \sin(\alpha +\beta )=\sin(\alpha )\cos(\beta )+\cos(\alpha )\sin(\beta )}$
${\displaystyle \sin(\alpha -\beta )=\sin(\alpha )\cos(\beta )-\cos(\alpha )\sin(\beta )}$

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