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

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)-sin(A+B) sin(A-B)=cos 2A.

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

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 :(tan(A+B))/(cot(A-B))=(sin^(2)A-sin^(2)B)/(cos^(2)A-sin^(2)B)

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

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

Prove (i)cos(A+B)+cos(A-B)=2cos A cos B(ii)cos(A-B)-cos(A+B)=2sin A sin B