Question

Please help!! Verify the identity.

cos (x - y) - cos (x + y) = 2 sin x sin y

Answer 1

Verify or prove? :)
Anyway, use these identities, which are actually practically the same identity :)
\[\large \cos(x+y)=\cos \ x\cos \ y - \sin \ x\sin\ y \]\[\large \cos(x-y)=\cos \ x\cos \ y+\sin \ x \sin\ y\]

Answer 2

multuply the first equation by -1, then add two equation, you will find the equation that you are looking for..