## watchmath 4 years ago Without L'hospital, compute $\lim_{x\to 0}\frac{\cos(\frac{\pi}{2}\cos x)}{\sin(\sin x)}$

1. Zarkon

use $\cos(\frac{\pi}{2}\cos(x))=\sin\left(\frac{\pi}{2}\cos(x)+\frac{\pi}{2}\right)$

2. watchmath

you mean sin(pi/2 - (pi/2)cosx)?

3. Zarkon

you can use that too.... then use the fact that $\lim_{x\to 0}\frac{\sin(x)}{x}=1$