设f(x)=sin(x+θ)+cos(x-θ)为偶函数,-π/2〈θ〈0,则θ=
问题描述：
设f(x)=sin(x+θ)+cos(x-θ)为偶函数,-π/2〈θ〈0,则θ=
答
因为f(x)=sin(x+θ)+cos(x-θ)为偶函数所以f(-x)=sin(-x+θ)+cos(-x-θ)=sin(-x)cosθ+cos(-x)sinθ+cosxcosθ-sinxsinθ=cosθ(cosx-sinx)+sinθ(cosx-sinx)=(cosx-sinx)(cosθ+sinθ)f(x)=sin(x+θ)+cos(x-θ)=sin...