This one has my entire class stumped:

$\displaystyle \lim_{x\rightarrow0}\frac{\sin(\tan(x))-\tan(\sin(x))}{\arcsin(\arctan(x))-\arctan(\arcsin(x))}=$

I've tried l'Hôpital but I still get $\displaystyle \frac{0}{0}$, and trying to build Taylor sums out of this mess seems impossible. I thought of using the squeeze theorem, but I have no idea what to squeeze it between or how to prove it. My attempt with l'Hôpital showed me it was>0, and graphing it on my computer it looked to be about 1. Any help writing a proof will be greatly appreciated.