a/sinA=b/sinB=c/sinC=2R=12
a=12sinA ,b=12sinB ,c=12sinC
a,b,c成等差
2*12sinB=12sinA+12sinC
sinA=2sinB-sinC
(3a-c)/b=(3*12sinA-12sinC)/12sinB=(3sinA-sinC)/sinB
=[3(2sinB-sinC)-sinC]/sinB
=(6sinB-4sinC)/sinB=cosC/cosB
sinBcosC=6sinBcosB-4sinCcosB
sinBcosC+sinCcosB=6sinBcosB-3sinCcosB
sin(B+C)=6sinBcosB-3sinCcosB
sin(180-A)=6sinBcosB-3sinCcosB
sinA=6sinBcosB-3sinCcosB
2sinB-sinC=3cosB(2sinB-sinC)
(2sinB-sinC)(3cosB-1)=0
cosB=1/3,2sinB-sinC=0,即sinA=0
0