If A+B+C=0 find maximum value of sinA+sinB+sinC

Hello Sudarshan

sinA + sinB +sinC=2sin[(A+B)/2].cos[(A-B)/2]+2sin(C/2).cos(C/2)

                      A+B+C=0=>A+B=-C

Therefore

             sinA + sinB +sinC=2sin(C/2).cos[(A+B)/2]-2Sin(C/2).cos[(A-B)/2]

                                     =2sin(C/2).{cos[(A+B)/2]-cos[(A-B)/2}

                                     =2sin(A/2).sin(B/2).sin(C/2)