f(x)=2√3sinxcosx+cos2x
=√3sin2x+cos2x
=2(√3/2sin2x+1/2cos2x)
=2sin(2x+π/6)
f(π/6)=2sin(2*π/6+π/6)
=2sin(3*π/6)
=2sinπ/2
=2��X�ʣ�0����/4��������f(x)��ֵ�򡣡�����ллX∈（0，π/4）2x∈（0，π/2）2x+π/6∈（π/6，π/2+π/6）1/2<=sin(2x+π/6)<=11<=2sin(2x+π/6)<=2∴f(x)的值域是[1,2]