因为 a/sinA= b/sinB = c/ sinC =2R
所以由原式得
2RsinC = 2RsinB(1+2CosA)
sinC = sinB(1+2CosA)
又
sinC = sin (180 - A - B)=sin(A+B)
所以sin(A+B)=sinB(1+2CosA)
sinAcosB + cosAsinB = sinB + 2sinBcosA
sinAcosB - cosAsinB = sinB
sin(A-B)=sinB
又 0 < A,B < 180
所以 A-B = B 则 A = 2B