解：f(x)=sin2x+cos2xcosπ/6+sinπ/6sin2x=sin2x+cos2x*√3/2+1/2sin2x=3/2sin2x+√3/2cos2x=√3sin(2x+π/6）0≤x≤π/2π/6≤2x+π/6≤7π/6所以最大值为当2x+π/6=π/2时，即x=π/6时取到最大值√3
