f(x)=sin2xcosπ/6+cos2xsinπ/6+sin2xcosπ/6-cos2xsinπ/6+2cos²x
=2sin2xcosπ/6+1+cos2x
=√3sin2x+cos2x+1
=2sin(2x+π/6)+1
1.f(x)最大值为2+1=3
2.f(a+b)=2sin[2(a+b)+π/6]+1=1
sin[2(a+b)+π/6]=0
2(a+b)+π/6=kπ
a+b=kπ/2-π/12 k=0.1.2.
3.f(x)≥2
f(x)-2=2sin(2x+π/6)-1≥0
sin(2x+π/6)≥1/2
x∈[kπ,π/3+kπ],k=0.1.2.