∵ cos2x=2cos²x-1
∴ cos²x=(cos2x+1)/2
∵ sin2x=2sinxcosx
∴ f(x)=√3sinxcosx-cos²x+1/2
=√3/2sin2x-1/2cos2x-1/2+1/2
=√3/2sin2x-1/2cos2x
=sin2xcosπ/6-sinπ/6cos2x
=sin(2x-π/6)
(1) 函数f(x)的最小正周期为：2π/2=π
(2) 单调增：2kπ-π/2<2x-π/6≤π/2+2kπ
2kπ-π/3<2x≤2π/3+2kπ
即 kπ-π/6
2kπ+2π/3<2x≤5π/3+2kπ
即 kπ+π/3
f(x)∈(-1/2，1]
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