(1＋tanx)/(1－tanx)=1＋sin2x
tan(x＋π/4)=(sinx＋cosx)²
sin(x＋π/4)/cos(x＋π/4)=2sin²(x＋π/4)
sin(x＋π/4)－sin(x＋π/4)sin(2x＋π/2)=0
sin(x＋π/4)[sin(2x＋π/2)－1]=0
sin(x＋π/4)[cos2x－1]=0
则：x＋π/4=kπ或2x=2kπ,解得x=kπ－π/4或x=kπ.其中k是整数.