If A, B, C are angles in a triangle, then prove that sinA+sinB+sinC=4 cos(A/2)cos(B/2)cos(C/2), sinA+sinB-sinC=4 sin(A/2) sin(B/2) cos(C/2), cosA+cosB+cosC=1+ 4 sin(A/2) sin(B/2) sin(C/2), cosA+cosB-cosC=-1+ 4 cos(A/2) cos(B/2)sin(C/2) #Trigonometry transformation formulas exercise 6(f)