## Precalculus (6th Edition) Blitzer

The formula $\sin \alpha -\sin \beta =2\sin \frac{\alpha -\beta }{2}\cos \frac{\alpha +\beta }{2}$ can be used to change the difference between two sines into the product of sines and cosines expressions.
$\sin \alpha -\sin \beta =2\sin \frac{\alpha -\beta }{2}\cos \frac{\alpha +\beta }{2}$ Thus, the above identity sum to product formula reflects that the difference of two sines is equal to the twice of the product of the sines and cosines expression.