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# Sum and differences identities

These sum and differences identities are very useful whenever expressions involving trigonometric functions need to be simplified.

$$\sin(\alpha \pm \beta)=\sin\alpha\cos\beta \pm \cos\alpha\sin\beta$$ $$\cos(\alpha \pm \beta)=\cos\alpha\cos\beta \mp \sin\alpha\sin\beta$$ $$\tan(\alpha \pm \beta)=\frac{\tan\alpha \pm \tan\beta}{1 \mp \tan\alpha \tan\beta}$$ $$\cot(\alpha \pm \beta)=\frac{\cot\alpha \cot\beta\mp 1}{\cot\beta \pm \tan\alpha}$$

2020-11-28