Prove that `sin(A+B)sin(A-B)=cos^2B-cos^2A`

Prove that sin(A+B)sin(A-B)=sin^(2)A-sin^(2)B=cos^(2)B-cos^(2)A

Prove that cos(A+B)cos(A-B)=cos^(2)A-sin^(2)B=cos^(2)B-sin^(2)A

Prove that: (sin(A+B)+sin(A-B))/(cos(A+B)+cos(A-B))=tan A

Prove that : sin^(2)Acos^(2)B-cos^(2)Asin^(2)B=sin^(2)A-sin^(2)B

Prove that: i) sin(A+B)cos(A-B)-cos(A+B)sin(A-B)=sin2B ii) cos(45^(@)-A)cos(45^(@)-B)-sin(45^(@)-A)sin(45^(@)-B)=sin(A+B)

Prove that: sin^(2)A=cos^(2)(A-B)+cos^(2)B-2cos(A-B)cos A cos B

Prove that: (sin(A+B)-2sinA+sin(A-B))/(cos(A+B)-2cosA+cos(A-B))= tanA

Prove that ((sin 2A -sin 2B)/(cos2A + cos 2B))^(n) + ((cos 2A - Cos 2B)/(sin 2A + sin 2B))^(n) = 2 tan^(n) (A-B) or 0 According as n is even or n is odd.

Prove that sin(A+B+C)=sin A cos B cos C+cos A sin B cos C+cos A cos B sin C-sin A sin B sin Ccos(A+B+C)=cos A cos B cos C-cos A sin B sin C-sin A cos B sin C-sin A sin B cos C

Prove that (sin^Acos^B-cos^2Asin^2B)=(sin^2A-sin^2B)