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f(x)
=sinx(sinx+根号3cosx)-1/2
=根号3sinxcosx+sinxsinx-1/2
=根号3/2sin2x+(1-cos2x)/2-1/2
=根号3/2sin2x-1/2cos2x
=sin(2x-π/6)
故最小正周期T=2π/2=π
单调增区间是：2Kπ-π/2<=2X-π/6<=2Kπ+π/2
即Kπ-π/6<=X<=Kπ+π/3
=sinx(sinx+根号3cosx)-1/2
=根号3sinxcosx+sinxsinx-1/2
=根号3/2sin2x+(1-cos2x)/2-1/2
=根号3/2sin2x-1/2cos2x
=sin(2x-π/6)
故最小正周期T=2π/2=π
单调增区间是：2Kπ-π/2<=2X-π/6<=2Kπ+π/2
即Kπ-π/6<=X<=Kπ+π/3
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