已知函数f(x)=sin(x-π/6)cosx,x属于(0,π/2) (1)求函数f(x)的值域 (2)若曲线f(x)在x0处的切线的倾斜角已知函数f(x)=sin(x-π/6)cosx,x属于(0,π/2)(1)求函数f(x)的值域(2)若曲线f(x)在x0处的切线的倾斜角α

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已知函数f(x)=sin(x-π/6)cosx,x属于(0,π/2) (1)求函数f(x)的值域 (2)若曲线f(x)在x0处的切线的倾斜角已知函数f(x)=sin(x-π/6)cosx,x属于(0,π/2)(1)求函数f(x)的值域(2)若曲线f(x)在x0处的切线的倾斜角α
已知函数f(x)=sin(x-π/6)cosx,x属于(0,π/2) (1)求函数f(x)的值域 (2)若曲线f(x)在x0处的切线的倾斜角
已知函数f(x)=sin(x-π/6)cosx,x属于(0,π/2)
(1)求函数f(x)的值域
(2)若曲线f(x)在x0处的切线的倾斜角α属于[arctan1/2,π/4],求x0的取值范围

已知函数f(x)=sin(x-π/6)cosx,x属于(0,π/2) (1)求函数f(x)的值域 (2)若曲线f(x)在x0处的切线的倾斜角已知函数f(x)=sin(x-π/6)cosx,x属于(0,π/2)(1)求函数f(x)的值域(2)若曲线f(x)在x0处的切线的倾斜角α
(1)
f(x)=(sinxcosπ/6+cosxsinπ/6)cosx
=sinxcosxcosπ/6+cos²xsinπ/6
=1/2*sin2xcosπ/6+1/2(cos2x+1)sinπ/6
=1/2(sin2xcosπ/6+cos2xsinπ/6)+1/2sinπ/6
=1/2sin(2x+π/6)+1/4
∵-1