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# C3 trig problem. watch

1. My brain is dead after not thinking for 4 weeks and part of the answer in the back of the book doesn't make sense to me.

Q. Prove the identity

cos(A+B)cos(A-B)=cos2A-sin2B

The solution given is this. The bit I don't understand is in bold.

LHS=[cosAcosB-sinAsinB]*[cosAcosB+sinAsinB]

=cos2Acos2B-sin2Asin2B

=cos2Acos2B-(1-cos2A)sin2B

=cos2A(cos2B+sin2B)-sin2B

=cos2A-sin2B

=RHS

I can't work out where that comes from the previous step.

Excuse me being thick.
2. They have just expanded it and then factorised.
3. (Original post by CalculusMan)
They have just expanded it and then factorised.
Oh I get it now. Thanks.

I told you my brain was dead.
4. Multiply out the bracket

cos2Acos2B-(1-cos2A)sin2B
= cos2Acos2B - sin2B + sin2Bcos2A

Take out a common factor of cos2A

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