Question

Without L'hospital, compute
\[\lim_{x\to 0}\frac{\cos(\frac{\pi}{2}\cos x)}{\sin(\sin x)}\]

Answer 1

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

Answer 2

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

Answer 3

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