求证:函数f(x)sin(x+θ)为偶函数的充要条件是θ=kπ+π/2(k∈Z)
φ=kπ+π/2(k∈Z)
f(x)=sin(ωx+kπ+π/2)
=coswx=cos(-wx)所以是充分条件
必要条件f(x)=f(-x)
sin(ωx+φ)=sin(-ωx+φ)
sin(ωx+φ)+sin(-ωx+φ)=0……………………………………这步怎么来的?
2sinφcoswx=0
sinφ=0
φ=kπ+π/2(k∈Z)