解f(x)=2sinx(sinx+cosx)=2sinxcosx+2sin²x=sin2x-(1-2sin²x)+1=sin2x-cos2x+1=√2(√2/2sin2x-√2/2cos2x)+1=√2(sin2xcosπ/4-cos2xsinπ/4)+1=√2sin(2x-π/4)+1当-π/2+2kπ≤2x-π/4≤π/2+2kπ即-π...