f （x)=√3/2sinxcosx- 3/2sin^2x+3/4
=√3/2sinxcosx- 3/2(1-cos2x)/2+3/4
=√3/2sinxcosx- 3/4(1-cos2x)+3/4
=√3/2sinxcosx- 3/4+3/4cos2x+3/4
=√3/4sin2x+3/4cos2x
=√3/2(1/2sin2x+√3/2cos2x)
=√3/2(sin2xcosπ/3+cos2xsinπ/3)
=√3/2sin(2x+π/3)
2kπ-π/2<2x+π/3<2kπ+π/2,单调递增区间
2kπ-5π/6<2x<2kπ+π/6
kπ-5π/12
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