Sum to product identities

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

$$\sin\alpha + \sin\beta=2\sin\frac{\alpha + \beta}{2}\cos\frac{\alpha - \beta}{2}$$ $$\sin\alpha - \sin\beta=2\sin\frac{\alpha - \beta}{2}\cos\frac{\alpha + \beta}{2}$$ $$\cos\alpha+\cos\beta=2\cos\frac{\alpha+\beta}{2}\cos\frac{\alpha-\beta}{2}$$ $$\cos\alpha-\cos\beta=2\sin\frac{\alpha+\beta}{2}\sin\frac{\beta-\alpha}{2}$$

2020-11-28