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