I was working through some trig exercises when I stumbled upon the following problem:
Prove that: $ \cos(A+B) \cdot \cos(A-B)=\cos^2A- \sin^2B$.
I started out by expanding it such that $ \cos(A+B) \cdot \cos(A-B)=(\cos A \cos B-\sin A \sin B) \cdot (\cos A \cos B+ \sin A \sin B),$ which simplifies to: $ \cos^2 A \cos^2 B- \sin^2 A \sin^2 B .$ However, I don't know how to proceed from here. Does anyone have any suggestions on how to continue.