a.b.c分别为三角形ABC的角A.角B.角C的对边,a(cosC)+根号3乘a(sinC)-b-c=0.求角A

由正弦定理,sinAcosC+√3sinAsinC-sinB=sinC,
sinAcosC+√3sinAsinC-sin(A+C)=sinC,
sinAcosC+√3sinAsinC-sinAcosC-cosAsinC=sinC,
√3sinAsinC-cosAsinC=sinC,sinC≠0,
√3sinA-cosA=1,2sin(A+30度)=1,
A+30度=30度,或 A+30度=150度,
所以,A=0（舍）,A=120度.