∵a+c=2b
利用正弦定理,a/sinA=b/sinB=c/sinC
∴ 2RsinA+2RsinC=4RsinB
即sinA+sinC=2sin(A+C)
∴2sin[(A+C)/2]cos[(A-C)/2]=4sin[(A+C)/2]cos[(A+C)/2]
∴ cos[(A-C)/2]=2cos[(A+C)/2]
即 cos30°=2sin(B/2)
∴ sin(B/2)=√3/4
∴ cos(B/2)=√(1-3/16)=√13/4
∴ sinB=2sin(B/2)cos(B/2)=√39/8