已知函数f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+/4),(1)求函数的最小正周期和对称轴方程(2)求函数在区间【-/12,π/2】的值域
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![已知函数f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+/4),(1)求函数的最小正周期和对称轴方程(2)求函数在区间【-/12,π/2】的值域](/uploads/image/z/404476-52-6.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dcos%282x-%CF%80%2F3%29%2B2sin%28x-%CF%80%2F4%29sin%28x%2B%2F4%29%2C%281%EF%BC%89%E6%B1%82%E5%87%BD%E6%95%B0%E7%9A%84%E6%9C%80%E5%B0%8F%E6%AD%A3%E5%91%A8%E6%9C%9F%E5%92%8C%E5%AF%B9%E7%A7%B0%E8%BD%B4%E6%96%B9%E7%A8%8B%EF%BC%882%EF%BC%89%E6%B1%82%E5%87%BD%E6%95%B0%E5%9C%A8%E5%8C%BA%E9%97%B4%E3%80%90-%2F12%2C%CF%80%2F2%E3%80%91%E7%9A%84%E5%80%BC%E5%9F%9F)
已知函数f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+/4),(1)求函数的最小正周期和对称轴方程(2)求函数在区间【-/12,π/2】的值域
已知函数f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+/4),(1)求函数的最小正周期和对称轴方程
(2)求函数在区间【-/12,π/2】的值域
已知函数f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+/4),(1)求函数的最小正周期和对称轴方程(2)求函数在区间【-/12,π/2】的值域
f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4)
=cos2xcosπ/3+sin2xsinπ/3+2(sinxcosπ/4-cosxsinπ/4)(sinxcosπ/4+cosxsinπ/4)
=(1/2)cos2x+(√3/2)sin2x+2[(√2/2)sinx-(√2/2)cosx][(√2/2)sinx+(√2/2)cosx]
=(1/2)cos2x+(√3/2)sin2x+(sinx)^2-(cosx)^2
=(1/2)cos2x+(√3/2)sin2x-cos2x
=(√3/2)sin2x-(1/2)cos2x
=sin(2x-π/6)
(1)最小正周期为T=2π/2=π.
2x-π/6=kπ+π/2,则对称轴方程为x=kπ/2+π/3,k为整数.
(2)-π/12