构造f(x)=tanx-x+x^3/3f'(x)=1/(cosx)^2-1+x^2=(sinx)^2/(cosx)^2+x^2=(tanx)^2+x^2≥0所以f(x)在(0,+∞)为增函数所以f(x)>f(0)=0所以tanx>x-x^3/3
