Prove that `sin(A+B)-cosC=cos(A+B)+sinC`

Prove that (sin(B-C))/(cosB cosC)+(sin(C-A))/(cosC cosA)+(sin(A-B))/(cosA cosB) =0 .

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

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

Prove that: sin(B-C)cos(A-D)+sin(C-A)cos(B-D)+sin(A-B)cos(C-D)

If A+B+C=pi , prove that : cosA + cosB-cosC=4cos(A/2) cos(B/2) sin(C/2) -1

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

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 cos(A+B) cos(A-B)-sin(A+B) sin(A-B)=cos 2A.

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