egin{align*}&lim_{x o0^+}cot x(frac{1}{sin x}-frac{1}{x})\ =&lim_{x o0^+}frac{x-sin x}{xsin x an x}\ =&lim_{x o0^+}frac{frac{1}{3!}x^3+o(x^3)}{x^3}cos x\ =&frac{1}{6}end{align*}
egin{align*}&lim_{x o0^+}cot x(frac{1}{sin x}-frac{1}{x})\ =&lim_{x o0^+}frac{x-sin x}{xsin x an x}\ =&lim_{x o0^+}frac{frac{1}{3!}x^3+o(x^3)}{x^3}cos x\ =&frac{1}{6}end{align*}