sinA,sinB,sinC和A,B,C都成等差数列,则2B=A+C, B=60°, A+C=120°.又2 sinB=sinA+sinC,2sin60°=2sin[(A+C)/2]cos[(A-C)/2],2sin60°=2sin60°cos[(A-C)/2],cos[(A-C)/2]=1,A=C,所以三角形是等边三角形....