f﹙x﹚＝cos²﹙x－π/6﹚－1/2cos2x
=[1+cos2(x－π/6)]/2 -(cos2x)/2
=1/2+[cos(2x-π/3)-cos2x]/2
=1/2+sin[(2x-π/3+2x)/2]sin[(2x-π/3-2x)/2]
=1/2- 1/2*sin(2x-π/6)
最小T=2π/2=π,对称轴为2x-π/6=nπ的时候,即x=nπ/2 +π/12,比如x=π/12就是一条对称轴.
-π/12≤x≤π/2,则-π/3≤2x-π/6≤5π/6,
-√3/2≤sin(2x-π/6)≤1,-1/2≤1/2- 1/2*sin(2x-π/6)≤ (2+√3)/4,
值域就是[-1/2,(2+√3)/4]