△ABC中,证明( b-c )sinA+( c-a )sinB+( a-b )sinC = 0

问题描述:

△ABC中,证明( b-c )sinA+( c-a )sinB+( a-b )sinC = 0

利用正弦定理:a / sinA = b / sinB = c / sinC = 2R(R为三角形外接圆的半径)所以:sinA = a / 2RsinB = b / 2RsinC = c / 2R代入,得:( b-c )sinA+( c-a )sinB+( a-b )sinC= (b - c)*a / 2R + (c - a)*b / 2R + (...