## Precalculus (6th Edition) Blitzer

$\sin \alpha \cos \beta =\frac{1}{2}\left[ \sin \left( \alpha +\beta \right)+sin\left( \alpha -\beta \right) \right]$ is one of the product-to-sum formulas, which reflects that the product of a sine and a cosine is equal to the half of the sum of the two sines expression. Now, consider another product-to-sum formula, that is $\sin \alpha \sin \beta =\frac{1}{2}\left[ \cos \left( \alpha -\beta \right)-\cos \left( \alpha +\beta \right) \right]$. So, this formula reflects that the product of two sines is equal to half of the difference between the two cosines expression. Thus, both product-to-sum formulas appear to be similar. It creates confusion, and thus, it becomes difficult to memorize.