f(x)=cos(根号3*x+θ)-根号3*sin(根号3*x+θ)是偶函数,那么θ可以取哪些值?A.π/6 B.π/3 C.-π/6 D.π/6D.π/6 改成-π/3

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f(x)=cos(根号3*x+θ)-根号3*sin(根号3*x+θ)是偶函数,那么θ可以取哪些值?A.π/6B.π/3C.-π/6D.π/6D.π/6改成-π/3f(x)=cos(根号3*x+θ)-根

f(x)=cos(根号3*x+θ)-根号3*sin(根号3*x+θ)是偶函数,那么θ可以取哪些值?A.π/6 B.π/3 C.-π/6 D.π/6D.π/6 改成-π/3
f(x)=cos(根号3*x+θ)-根号3*sin(根号3*x+θ)是偶函数,那么θ可以取哪些值?
A.π/6 B.π/3 C.-π/6 D.π/6
D.π/6 改成-π/3

f(x)=cos(根号3*x+θ)-根号3*sin(根号3*x+θ)是偶函数,那么θ可以取哪些值?A.π/6 B.π/3 C.-π/6 D.π/6D.π/6 改成-π/3
f(x)=cos(根号3*x+θ)-根号3*sin(根号3*x+θ)
=2{(1/2)cos(根号3*x+θ)-[(根号3)/2]*sin(根号3*x+θ)}
=2cos(根号3*x+θ+π/3)
由于该函数是偶函数,所以f(-x)=f(x),即2cos[根号3*(-x)+θ+π/3]=2cos(根号3*x+θ+π/3)
于是θ=-π/3
故选D