Question

Verify the identity. Show your work.
cos(alpha-beta)-cos(alpha+beta)=2 sin alpha sin beta

Answer 1

We have the identity\[\cos(x\pm y)=\cos x\cos y\mp \sin x\sin y\]so the left hand side can be written as
\[(\cos\alpha\cos\beta+\sin\alpha\sin\beta)-(\cos\alpha\cos\beta-\sin\alpha\sin\beta)\]

Answer 2

thanks!