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...

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- Jan 22nd 2010, 03:05 AMPunchProve(5)
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... - Jan 22nd 2010, 04:37 AMmathaddict
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 $\displaystyle (a+b)(a-b)=a^2-b^2$

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

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

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