taking a limit and getting the wrong answer...don't know why

The limit in question: $\lim_{x \to 0} \frac{\tan(\tan x) - \sin(\sin x)}{\tan x - \sin x} = 2$ As stated in the TL;DR, I understand how to get to the correct answer, but I don't know that I would have figured it out without a little help/direction at the beginning because it involves adding... Read more