calculus - Using L'Hôpital's rule

Using L'Hôpital's rule to find

$$\lim_{x\to \infty} \left(\frac {\tan\beta x - \beta \tan x} {\sin\beta x - \beta \sin x}\right)$$
Where $\beta$ is a nonzero constant different from $\pm 1$.

I find this question weird because the limit does not confine to one of the forms that you can use L'Hôpital's rule. It is not one of the following form $\infty \over \infty$, $0 \over 0$, $\infty -\infty$, $0\times \infty$, $1^\infty$, $\infty^0$. So we cannot directly use the rule. How do I justify this question?