a/sinA=b/sinB=c/sinC=2R
所以:a=2RsinA, b=2RsinB, c=2RsinC
而：sinC=sin(pi-(A+B))=sinAcosB+cosAsinB
acosB2的平方+bcosA2的平方
=(a(cosB+1)/2)+(b(cosA+1)/2)
=3c/2
所以：(a+b)+acosB+bcosA=3c
(sinA+sinB)+sinAcosB+cosAsinB=3sinC
(sinA+sinB)+sinC=3sinC
sinA+sinB=2sinC
a+b=2c
即a,b,c成等差数列