Question

prove that,cos^2 (A+B)-sin^2 (A-B)=Cos2a cos2b




A cos2B

Answer 1

sin2(A-B) - sin2(A+B) =sin(A+A)sin(-B-B) [using formula ,sin2a-sin2b=sin(a-b)sin(a+b)]

=sin(-2B)sin2A=-sin2Asin2B

Now LHS becomes

= cos2Acos2B-sin2Asin2B [using formula ,cosacosb - sinasinb =cos(a+b)]

=cos(2A+2B)=cos2(A+B) = RHS

hence proved