Question

已知函数f(x)=√3·sin(ωx+ψ)－cos(ωx+ψ)(00)为偶函数,且函数y=f(x)图像的两相邻对称轴间的

Answer 1

f(x)=√3·sin(ωx+ψ)－cos(ωx+ψ)

=2(√3·sin(ωx+ψ)／2－cos(ωx+ψ)／2)

=2cos30°sin(ωx+ψ)－sin30°cos(ωx+ψ)

=2sin(ωx+ψ-π/6)

两相邻对称轴间的距离为π/2,即半周期,（ω>0)

故ω=2,

所以f(x)=2sin(2x+ψ-π/6)

是偶函数,则f（-x）=f（x）,

2sin(2x+ψ-π/6)=2sin(-2x+ψ-π/6),（0