cosA-2cosC)/cosB=(2c-a)/b根据正弦定理(cosA-2cosC)/cosB=(2sinC-sinA)/sinB∴sinBcosA-2cosCsinB=2sinCcosB-sinAcosB∴sinBcosA+cosBsinA=2(sinBcosC+cosBsinC)∴sin(B+A)=2sin(B+C)∴sinC=2sinA∴sinC/sinA=2∵sinC/sinA=2∴c/a=2.c=2a∵cosB=1/4,b=2,根据余弦定理b=a+c-2accosB∴4=a+4a-a==>a=1,c=2又sinB=√(1-cosB)=√15/4∴三角形ABC的面积S=1/2acsinB=1/2*2*√15/4=√15/4