Prove that
`sin (A+B)=cos [\pi/2-(A+B)]`

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

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

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

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

Prove that : (1+sin 2A)/(cos 2A) = (cos A + sin A)/(cos A - sin A) = tan (pi/4 + A)

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

Prove that: sin ((8pi)/3) cos ((23pi)/6)+cos ((13pi)/3) sin ((35pi)/6)=1/2

Prove that: cos(pi/4-A)cos(pi/4-B)-sin(pi/4-A)sin(pi/4-B)="sin"(A+B)

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