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

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

(sin(A+3B)+sin(3A+B))/(sin2A+sin2B)=2cos(A+B)

(sin(A+3B)+sin(3A+B))/(sin2A+sin2B)=2cos(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(A+B) cos(A-B)-sin(A+B) sin(A-B)=cos 2A.

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

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

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