Question

已知函數.

(Ⅰ)求f(x)的最大值及最小正周期；

(Ⅱ)求使f(x)≥2的x的取值范圍

Answer 1

解：（Ⅰ）∵f(x)=sin(2x+)+sin(2x-)+2cos²x

               =sin2xcos+cos2xsin+sin2xcos-cos2xsin+cos2x+1

               =sin2x+cos2x+1

               = 2sin(2x+)+1

         ∴f(x)_max=2+1=3

          

（Ⅱ）∵f(x)≥2

       ∴ 2sin(2x+)+1≥2

      ∴sin(2x+)≥

      ∴ 2kx+≤2x+≤2k+

         k≤x≤k+(k∈Z)

      ∴使f(x) ≥2的x的取值范圍是{x|k≤x≤k+,k∈Z}