由正弦定理,由b^2=ac可得sin^2(B)=sinA*sinC
由于三角形中A+B+C=180,则B=180-(A+C)
cos(A-C)+cosB
=cos(A-C)+cos(180-(A+C))
=cosAcosC+sinAsinC-cos(A+C)
=cosAcosC+sinAsinC-(cosAcosC-sinAsinC)
=2sinAsinC
=3/2
所以sinAsinC=3/4
即sin^2(B)=3/4
sinB=√3/2
所以B=60或B=120
由正弦定理,由b^2=ac可得sin^2(B)=sinA*sinC
由于三角形中A+B+C=180,则B=180-(A+C)
cos(A-C)+cosB
=cos(A-C)+cos(180-(A+C))
=cosAcosC+sinAsinC-cos(A+C)
=cosAcosC+sinAsinC-(cosAcosC-sinAsinC)
=2sinAsinC
=3/2
所以sinAsinC=3/4
即sin^2(B)=3/4
sinB=√3/2
所以B=60或B=120