\begin{multline*}
      \lxtoo\frac{\tg x-x}{x-\sin x}\lh
      \lxtoo\frac{\frac1{\cos^2x}-1}{1-\cos x}=
      \lxtoo\frac{1-\cos^2x}{(\cos^2x)(1-\cos x)}=\\
      =\lxtoo\frac{(1-\cos x)(1+\cos x)}{(\cos^2x)(1-\cos x)}=
      \lxtoo\frac{1+\cos x}{cos^2x} = 2.
   \end{multline*}\\