Question

设函数f(x)=sin(wx+φ)+cos(wx+φ)(w>0,|φ|<π/2)的最小正周期为π，且f(-x)=f(x)则

A f(x)在（0，π/2)单调递减。
B f(x)在（π/4, 3π/4)单调递减。
C f(x)在(0,π/2）单调递增。
D f(x)在（π/4,3π/4)单调递增
PS:完整解题过程

Answer 1

f(x)=sin(wx+φ)+cos(wx+φ)
=√2sin(wx+φ+π/4)
T=2π/w=π
w=2
f(x)=√2sin(2x+φ+π/4)
f(-x)=f(x),
所以 f(-π/8)=f(π/8)
sinφ=sin(π/2+φ)=cosφ
tanφ=1
|φ|<π/2
φ=π/4
f(x))=√2sin(2x+π/4+π/4)=√2sin(2x+π/2)=√2cos2x
作出图像，选A