Prove(5)

Quote:

Originally Posted by Punch

Prove $cos^2A-cos^2B=sin(B-A)sin(B+A)$

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 .

$(\sin B\cos A-\cos B\sin A)(\sin B\cos A+\cos B\sin A)$

this is in the form of $(a+b)(a-b)=a^2-b^2$

$\sin^2 B\cos^2 A-\cos^2 B\sin^2 A$

$(1-\cos^2 B)\cos^2 A-\cos^2 B(1-\cos^2 A)$

$\cos^2 A-\cos^2 A\cos^2 B-\cos^2 B+\cos^2 B\cos^2 A$