一道极限题目

\begin{align*}

&\lim_{x\to0^+}\cot x(\frac{1}{\sin x}-\frac{1}{x})\\

=&\lim_{x\to0^+}\frac{x-\sin x}{x\sin x\tan x}\\

=&\lim_{x\to0^+}\frac{\frac{1}{3!}x^3+o(x^3)}{x^3}\cos x\\

=&\frac{1}{6}

\end{align*}