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

Prove that (sin A+sin B)/(cos A+cos B)+(cos A-cos B)/(sin A-sin B)=0

Prove that : (sin A - sin B)/ (cos A + cos B) + (cos A - cos B)/ (sin A + sin B) = 0

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

Prove that (sin(A+B)+sin(A-B))/(cos(A+B)+cos(A-B))=tanA

Prove that: (sin(B-C))/(cos B cos C)+(sin(C-A))/(cos C cos A)+(sin(A-B))/(cos A cos B)=0

Prove that (1 + sin A) / (cos A) + (cos B) / (1-sin B) = (2sin A-2sin B) / (sin (AB) + cos A-cos B)

Prove that sin (A+B)= sin A cos B + cos A sin B.

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: 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)

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)