在△ABC中,若sin^2B=sinAsinC,则cos2B+COSB+COS(A-C)=

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在△ABC中,若sin^2B=sinAsinC,则cos2B+COSB+COS(A-C)=

sin²B=sinAsinC.====>2sin²B=2sinAsinC.===>1-cos(2B)=cos(A-C)-cos(A+C).===>cos(2B)=1-cos(A-C)+cos(A+C)=1-cos(A-C)+cos(180º-B)=1-cos(A-C)-cosB.===>cos(2B)+cosB+cos(A-C)=1.