由A＋B＋C＝180度,A+C=2B,可得
3B＝180度
B＝60度
根据正弦定理,可得
a/sinA=b/sinB
1/sinA=√3/sin60
sinA=√3/2/√3=1/2
cos(A-C)+cosB
=cos(A-C)-cos(A+C)
=cosAcosC+sinAsinC-cosAcosC+sinAsinC
=2sinAsinC=3/2
sinAsinC=3/4
根据正弦定理,a/sinA=b/sinB=c/sinC=2R
b^2=4R^2sin^2B
a=2RsinA
c=2RsinC
因为b^2=ac
所以,sin^2B=sinAsinC=3/4
因为B