Question

cos 2A cos 2B + sin²(A - B) - sin²(A + B)​

Answer 1

Answer:

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

Answer 2

Step-by-step explanation:

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