已知函数f(x)=sin(x+θ)+3cos(x−θ)为偶函数,求θ的值.

问题描述:

已知函数f(x)=sin(x+θ)+

3
cos(x−θ)为偶函数,求θ的值.

f(x)为偶函数,则f(x)-f(-x)=0  (即恒等于0)⇒sin(x+θ)+3cos(x-θ)+sin(x-θ)-3cos(x+θ)=0⇒sin(x+θ-π3)+sin(x-θ+π3)=0⇒2sinxcos(θ-π3)=0⇒cos(θ-π3)=0⇒θ=kπ+π2+π3(k...