Prove $\displaystyle cos^2A-cos^2B=sin(B-A)sin(B+A)$
I attempted the question start with the RHS, using the addition formulae and ended off with cot^2A-cot^2B...
lets start from the RHS .
$\displaystyle (\sin B\cos A-\cos B\sin A)(\sin B\cos A+\cos B\sin A)$
this is in the form of $\displaystyle (a+b)(a-b)=a^2-b^2$
$\displaystyle \sin^2 B\cos^2 A-\cos^2 B\sin^2 A$
$\displaystyle (1-\cos^2 B)\cos^2 A-\cos^2 B(1-\cos^2 A)$
$\displaystyle \cos^2 A-\cos^2 A\cos^2 B-\cos^2 B+\cos^2 B\cos^2 A$