in triangle ABC ,show that sinA+sinB -sinC= 4 sin(A/2) sin(B2)sin(C2)

Dear Student,
Recheck your R.H.S. part.

L.H.S.=sinA+sinB-sinC=sinA+sinB-sinC=2sinA2cosA2+2cosB+C2sinB-C2=2sinA2cosπ2-B+C2+2cosπ2-A2sinB-C2=2sinA2sinB+C2+2sinA2sinB-C2=2sinA2sinB+C2+sinB-C2=2sinA22sinB+C2+B-C22cosB+C2-B-C22=2sinA22sinB2cosC2=4sinA2sinB2cosC2=R.H.S.Hence Proved.

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