已知函数f(x)=根号3sin(wx+fai)-cos(wx+fai)(0

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已知函数f(x)=根号3sin(wx+fai)-cos(wx+fai)(0
已知函数f(x)=根号3sin(wx+fai)-cos(wx+fai)(0

已知函数f(x)=根号3sin(wx+fai)-cos(wx+fai)(0
已知函数f(x)=(√3)sin(ωx+φ)-cos(wx+φ)(0

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(1).f(x)=(√3)sin(ωx+φ)-cos(wx+φ)=2[(√3/2)sin(ωx+φ)-(1/2)cos(ωx+φ)]=2[sin(ωx+φ)cos(π/6)-cos(ωx+φ)sin(π/6)]=2sin(ωx+φ-π/6)∵f(x)是偶函数，∴φ-π/3=π/2，即φ=π/3+π/3=5π/6，于是f(x)=2sin(ωx+π/2)=2cosωx.又∵函数y=f（x）图像的两相邻对称轴间的距离为π/2，∴其最小正周期为π，故ω=2.即f(x)=2cos2x，f(π/8)=2cos(π/4)=√2.(2)g(x)=2cos[2(x-π/6)]=2cos(2x-π/3).由2kπ<2x-π/3<2kπ+π，2kπ+π/3<2x<2kπ+4π/3，得单减区间kπ+π/6

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