f(x)=2sinxcosx—2(sinx)^2+1=sin2x+cos2x=√2(sin2xcos45°+cos2xsin45°)
=√2sin(2x+45°)
可见:T=2π/2=π
单调递增区间为:(kπ-3/8π,kπ+π/8)(k∈N)