Sum and Difference Formulas

Sum and Difference Formula for Cosine

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

$\cos(\alpha +\beta )=\cos(\alpha )\cos(\beta )-\sin(\alpha )\sin(\beta )$

$\cos(\alpha -\beta )=\cos(\alpha )\cos(\beta )+\sin(\alpha )\sin(\beta )$

Sum and Difference Formula for Sine

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

$\sin(\alpha +\beta )=\sin(\alpha )\cos(\beta )+\cos(\alpha )\sin(\beta )$

$\sin(\alpha -\beta )=\sin(\alpha )\cos(\beta )-\cos(\alpha )\sin(\beta )$

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