函数f(x)=2sin2x-2sinxcosx-根号3cos2x求最小正周期和最值

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函数f(x)=2sin2x-2sinxcosx-根号3cos2x求最小正周期和最值

函数f(x)=2sin2x-2sinxcosx-根号3cos2x求最小正周期和最值
函数f(x)=2sin2x-2sinxcosx-根号3cos2x求最小正周期和最值

函数f(x)=2sin2x-2sinxcosx-根号3cos2x求最小正周期和最值
f(x)=2sin2x-2sinxcosx-√3cos2x
=2sin2x-sin2x-√3cos2x
=sin2x-√3cos2x
=2(1/2sin2x-√3/2cos2x)
=2sin(2x+ψ)
T=2π/2=π
f(x)max=2 f(x)min=-2

π(-π/4-3π/4) ∵f(x)=√3cos2x+sin2x+1 =2sin(2x+π/3)+1 ∴f(x)的最小周期为π