f(x)=-√3sinx·cosx+cos²x
=-√3/2sin2x+(1+cos2x)/2
=-√3/2sin2x+1/2cos2x+1/2
=sin2xcos(5π/6)+cos2xsin5π/6 +1/2
=sin(2x+5π/6）+1/2
所以
最大值=1+1/2=3/2
最小值=-1+1/2=-1/2