## Precalculus (6th Edition) Blitzer

The formula $\sin \alpha \sin \beta =\frac{1}{2}\left[ \cos \left( \alpha -\beta \right)-\cos \left( \alpha +\beta \right) \right]$ can be used to change the product of two sines into the difference of two cosines expressions.
Let us consider the given formula: $\sin \alpha \sin \beta =\frac{1}{2}\left[ \cos \left( \alpha -\beta \right)-\cos \left( \alpha +\beta \right) \right]$ Thus, the above formula is a product-to-sum formula, which reflects that the product of two sines is equal to the half of the difference between the two cosines expression.