（1）由正弦定理，sin^B=sinAsinC,B=π/3,3/2=cos(A-C)-cos(A+C),A+C=2π/3,∴cos(A-C)=1,∴A=C=π/3.(2)|A-C|<2π/3,|A-C|/2<π/3,sinA+sinC=2sin[(A+C)/2]cos[(A-C)/2]=√3cos[(A-C)/2],其取值范围是(√3/2，√3].
