Answer
The formula $\sin \alpha \cos \beta =\frac{1}{2}\left[ \sin \left( \alpha +\beta \right)+sin\left( \alpha -\beta \right) \right]$ can be used to change the product of a sine and cosines into the sum of two sines expressions.
Work Step by Step
$\sin \alpha \cos \beta =\frac{1}{2}\left[ \sin \left( \alpha +\beta \right)+sin\left( \alpha -\beta \right) \right]$
The above identity or product sum formula reflects that the product of a sine and cosine is equal to the half of the sum of the two sines expression.
Thus, the formula $\sin \alpha \cos \beta =\frac{1}{2}\left[ \sin \left( \alpha +\beta \right)+sin\left( \alpha -\beta \right) \right]$ can be used to change the product of sines and cosines into the sum of two sines expressions.
