# Thread: Help me to prove this! My brainjuice is OVERHEATING!!!

1. ## Help me to prove this! My brainjuice is OVERHEATING!!!

Question:
Prove this identity.
1+cos2A-cos2B-cos2(A+B)=4sin(A+B)cosAcosB

HELP! I only able to proceed 1 step only, and then, it just go back to the question again when i further solving it! Dying...

2. $1+\cos 2A-\cos 2B-\cos 2(A+B)=2\cos^2A-2\cos\frac{2B+2(A+B)}{2}\cos\frac{2B-2(A+B)}{2}=$

$=2\cos^2A-2\cos(A+2B)\cos A=2\cos A(\cos A-\cos(A+2B))=$

$=2\cos A\cdot 2\sin\frac{A+2B-A}{2}\sin\frac{A+2B+A}{2}=$

$=4\cos A\sin B\sin(A+B)$

3. Thanks RedDog!
But is there any missing?

How it transform from
$1+\cos2A-\cos2B-\cos2(A+B)$
to this
$=2\cos^2A-2\cos(A+2B)\cos A$
?
(Perhaps can help me with explaining each other steps too?)