f(x)=sinxsin(x+π/2)-√3cos^2(3π+x)+√3/2
=sinxcosx-√3cos²x+√3/2
=1/2 sin2x- √3(1+cos2x)/2 +√3/2
=1/2 sin2x -√3/2 cos2x
=sin(2x-π/3)
增区间 2kπ-π/2 ≤2x-π/3≤2kπ+π/2
2kπ-π/6 ≤2x≤2kπ+5π/6
kπ-π/12 ≤x≤kπ+5π/12
所以增区间为
【 kπ-π/12 ,kπ+5π/12】,k是整数
f(x)=sinxsin(x+π/2)-√3cos^2(3π+x)+√3/2的增区间
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