calculus - Another limit to evaluate: $limlimits_{x to infty}frac{x-sin x }{x-tan x}$

How do you evaluate? $$\lim_{x \to \infty}\frac{x-\sin x }{x-\tan x}$$

The fact that x tends toinfty bothers me very much. I tried to "force a L'Hospital", because we know that the limit of a product between a function that tends to 0 and one that is bounded equals 0. So, how would you manage this limit?