hi , help please
If you're allowed to use L'Hospital's Rule, use it.
If not, rewrite it as
$\displaystyle \displaystyle \begin{align*} \frac{\tan{(x)} - \sin{(x)}}{x^3} &= \frac{\tan{(x)}}{x^3} - \frac{\sin{(x)}}{x^3} \\ &= \frac{\sin{(x)}}{x^3\cos{(x)}} - \frac{\sin{(x)}}{x^3} \\ &= \frac{\sin{(x)}}{x} \cdot \frac{1}{\cos{(x)}} \cdot \frac{1}{x^2} - \frac{\sin{(x)}}{x} \cdot \frac{1}{x^2} \end{align*}$
Go from there, using the well-known limit $\displaystyle \displaystyle \begin{align*} \lim_{x \to 0} \frac{\sin{(x)}}{x} = 1 \end{align*}$.