y=sin^2x+2sinxcosx+3cos^2x=sin^2x+3cos^2x+2sinxcosx =2cos²+1+sin2x =cos2x+2+sin2x =√2sin(2x+π/4)+2最小正周期为 2π/2=π单调增区间2x+π/4∈[2kπ-π/2,2kπ+π/2]x∈[kπ-3π/8,kπ+π/8]单调减区...