a⊥b
-f(x)+cos²wx+√3sinwxcoswx=0
f(x)=√3sinwxcoswx+cos²wx
=√3/2)sin2wx+(1/2)(1+cos2wx)
=(√3/2)sin2wx+(1/2)cos2wx+1/2
=sin(2wx+π/6)+1/2
最小正周期为：2π/2w=π/w
因为相邻两对称轴的距离等于半个周期
3π/2=π/2w==>w=1/3
f(x)=sin(2/3x+π/6)+1/2
-π≤x≤π/2
-π/2≤2/3x+π/6≤π/2
-1≤sin(2/3x+π/6)≤1
-1/2≤sin(2/3x+π/6)+1/2≤3/2
值域为：【-1/2,3/2】