高一数学三角函数，急急急

Question

如题所述

Answer 1

1、（1）2x+π/4≠π/2+kπ
2x≠π/4+kπ
定义域： x≠π/8+kπ/2
最小正周期：π/2
（2）tan(α+π/4)=2cos2α
(1+tanα)/(1-tanα)=2cos2α
(sinα+cosα)/(cosα-sinα)=2(cos²α-sin²α)
1/(cosα-sinα)=2(cosα-sinα)
(cosα-sinα)²=1/2
2cosαsinα=1/2
sin2α=1/2
α=π/6
2、f(x)=2sinx/4cosx/4+√3cosx/2
=sinx/2+√3cosx/2
=2(1/2sinx/2+√3/2cosx/2)
=2(sinx/2cosπ/3+sinπ/3cosx/2)
=2sin(x/2+π/3)
(1) 最小正周期：2π/(1/2)=4π
最大值：2
(2) g(x)=f(x+π/3)
g(x)=2sin(x/2+π/2)
=-2cos(x/2)
g(-x)=g(x) 为偶函数