,{sin(A-B)+sinC)/{cos(A-B)+cosC}
=,{sin(A-B)+sin(A+B))/{cos(A-B)-cos(A+B)}
=2sinAcosB/2sinAsinB
=cosB/sinB
=√3/3
B=30°.
a/sinA=b/sinB=c/sinC,asinB=bsinA=√3sinA,b=√3.
a+c=2√3(sinA+sinC)=4√3sin[(A+C)/2]cos[(A-C)/2]
=4√3sinBcos[(A-C)/2]
=2√3cos[(A-C)/2],当A=C时,a+c取最大值：2√3.