2acosC+c=2b

正弦定理   2sinAcosC+sinC=2sinB          

sinB=sin(A+C)=sinAcosC+cosAsinC

2sinAcosC+sinC=2sinAcosC+2cosAsinC

所以   sinC=2cosAsinC              

cosA=1/2       sinA=√3/2           tanA=sinA/cosA=√3

余弦定理    a^2=b^2+c^2-2bc*cosA

a^2=bc       bc=b^2+c^2-2bc*cosA

b^2+c^2-2bc=0                ( b-c)^2=0

b=c       a^2=bc

所以    a=b=c

所以   C=60°