根据正弦定理有:a/sinA=b/sinB=c/sinC,由abc成等差数列知：sinA,sinB,sinC也成等差数列，于是有:sinA+sinC=2sinB,由三角形内角和为180°可得：sinB=sin(180°-A-C)=sin(A+C)=sinAcosC+cosAsinC,于是有：sinA+sinC=2sinAcosC+2cosAsinC,整理的:sinA(1-2cosC)=sinC(1-2cosA),两边平方:sin2A(2cosA-1)2=sin2C(1-2cosA)2,利用sin2A+cos2A=1,展开得：(1-cos2C)(4cos2A-4c...
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