prove that sinA.sin(B-C)+sinB.sin(C-A)+sinC.sin(A-B)=0

prove that sinA.sin(B-C)+sinB.sin(C-A)+sinC.sin(A-B)=0 How to Solve In first step the formula of sin(a-b)=sina.cosb-cosa.sinb is putted. 2nd step - This step is simply easy of multiplication 3rd step - Arrange the following in regular manner and + and - terms are canceled out. 4th step - Hence the Answer is 0 5th step - Finally we proved that sinA.sin(B-C)+sinB.sin(C-A)+sinC.sin(A-B)=0