cos[2(arctanx-π/4)]=cos(2arctanx-π/2)=sin(2arctanx)=2tan(arctanx)/[1+tan(ractanx)^2]=2x/(1+x^2),x>=1,∴π/4<=arctanx<π/2，∴0<=2(arctanx-π/4)<π/2，∴2(arctanx-π/4)=arccos[2x/(1+x^2)],∴命题成立。
