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

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^(2) B-cos^(2) A

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

If (cos^4A)/(cos^2B)+(sin^4A)/(sin^2B)=1 then prove that (i)sin^4A+sin^4B=2sin^2Asin^2B (ii)(cos^4B)/(cos^2A)+(sin^4B)/(sin^2A)=1

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

Prove that sin^2 A cos^2 B+cos^2 A sin^2 B+cos^2 A cos^2 B+sin^2 A sin^2 B=1

Prove the following: sin(A+B).sin(A-B)=cos^2B-cos^2A

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