问题描述：
三角形ABC,对边分别为abc,cos(A-C)+cosB=3/2,b的平方等于ac,求角B
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=sin^B*4R^2 a=sinA*2R c=sinC*2R
所以,sin^B=sinA*sinC=3/4
因为B
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=sin^B*4R^2 a=sinA*2R c=sinC*2R
所以,sin^B=sinA*sinC=3/4
因为B
问题解答：
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