`(cos A+cos B)^(2)+(sin A-sin B)^(2)=4cos^(2)(A+B)/(2)`

Prove that (cos A + cos B ) ^(2) +(sin A + sin B) ^(2) = 4 cos ^(2) ((A -B)/(2)).

Prove that (cos A - cos B) ^(2) + (sin A - sin B ) ^(2) = 4 sin ^(2) ((A -B)/( 2 )).

Prove that ((cos A + cos B)/( sin A - sin B )) ^(n) + ((sin A + sin B )/( cos A - cos B )) ^(n) ={{:(2 cot ^(n) ((A- B)/(2)),"," "if n is even."),(0,",""if n is odd."):}.

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

Prove the following identities: tan^2A-tan^2B=(cos^2B-cos^2A)/(cos^2Bcos^2A)=(sin^2A-sin^2B)/(cos^2Acos^2B) (sinA-sinB)/(cosA+cosB)+(cosA-cosB)/(sinA+sinB)=0

Prove that (cos^(2)A-sin^(2)B)+1-cos^(2)C

If A, B, C are interior angles of DeltaABC such that (cos A + cos B + cos C)^(2)+(sin A + sin B + sin C)^(2)=9 , then number of possible triangles is

let a=cosA+cosB-cos(A+B) and b=4sin(A/2)sin(B/2)cos((A+B)/2) Then a-b is

If A and B are complementary angles, prove that : (sin A + sin B)/ (sin A - sin B) + (cos B - cos A)/ (cos B + cos A) = (2)/(2 sin^(2) A - 1)

Prove the following identities : tan^(2) A - tan^(2) B = (sin^(2) A - sin^(2) B)/ (cos^(2) A . cos^(2) B)