Prove that, `tan(A+B)=(sin(A+B))/(cos(A+B))`

Prove that: (sin(A+B)+"sin"(A-B))/(cos(A+B)+"cos"(A-B))=t a n A

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

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

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