正余弦定理的题:已知三角形ABC中,边a、b、c满足2b=a+c,且A-C=60度.求sinB的值?

由正弦定理:∵a+c=2b ∴sinA+sinC=2sinB=4sin(B/2)cos(B/2)又:sinA+sinC=2sin((A+C)/2)cos((A-C)/2)=2cos(B/2)cos((A-C)/2)∴4sin(B/2)=2cos((A-C)/2)===>sin(B/2)=cos30º/2=√3/4∴cos(B/2)=√13/4∴sinB=2sin...