`sin(A+B).sin(A- B)=sin^(2)A-sin^(2)B`

Show that: tan(A+B).tan(A-B)=(sin^(2)A-sin^(2)B)/(cos^(2)A-sin^(2)B).

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

If (cos^(4)A)/(cos^(2)B)+(sin^(4)A)/(sin^(2)B)=1, Prove that: sin^(4)A+sin^(4)B=2sin^(2)A sin^(2)B

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

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

Prove that sin^(2)(A+B)-sin^(2)(A-B)=sin2A*sin2B

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

If A+B+C= 180^(@) , prove that: (i) "sin"^(2)+"sin"^(2)B-"sin"^(2)C=2 "sin"A sin B cos C (ii) "sin"^(2)A-"sin"^(2)B+"sin"^(2) C=2 sin Acos B sin C.

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

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