2B=A+C
A+B+C=180°
3B=180°
B=60°
cos2A+cos2C=cos2A+cos2（120°-A）=cos2A+（-cosA/2+√3sinA/2）2
=cos2A+cos2A/4-√3sinAcosA/2+3sin2A/4
=5cos2A/4+3sin2A/4-√3sinAcosA/2
=3/4+（cos2A+1）/4-√3sin2A/4
=1+（cos2A/2+√3sin2A/2）/2
=1+sin（2A+30°）/2
设A为最小角,则A∈（0,60°）,则原式∈（5/4,3/2）