解先化简
由y=cos^2x-√3sinxcosx-1/2
=cos^2x-1/2-√3sinxcosx
=（2cos^2x-1）/2-√3/2×2sinxcosx
=1/2cos2x-√3/2sin2x
=cos（2x+π/3)
令2x+π/3=kπ,k属于X
解得x=kπ/2-π/6,k属于Z
故原函数的对称轴为x=kπ/2-π/6,k属于Z.