已知函数f(x)=2sinx cosx+√3 cos2x,求f(x)最小正周期

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已知函数f(x)=2sinx cosx+√3 cos2x,求f(x)最小正周期
已知函数f(x)=2sinx cosx+√3 cos2x,求f(x)最小正周期

已知函数f(x)=2sinx cosx+√3 cos2x,求f(x)最小正周期
f(x)=2sinx cosx+√3 cos2x
=sin2x+√3 cos2x
=2(sin2xcosπ/3+cos2xsinπ/3)
=2sin(2x+π/3)
f(x)最小正周期=2π/2=π

f(x)=2sinx cosx+√3 cos2x
=sin2x+√3 cos2x
=2sin(2x+π/3)
因此f(x)最小正周期为2π/2=π