What is $\lim\limits_{x \to 0} \frac{\sin(\pi \cos^2x)}{x^2}= \ ?$

Question

I need help with this problem

$\large \displaystyle \lim_{x \to 0} \dfrac{\sin(\pi \cos^2x)}{x^2}= \ ?$

A. $1$

B. $\pi$

C. $\dfrac{\pi}{2}$

D. $-\pi$

EDIT ::: In the light of hint by Mr @G. Sassatelli , here is my try

enter image description here

See this https://math.stackexchange.com/questions/744713/calculation-of-lim-x-rightarrow-0-frac-sin-pi-cos2-xx2?rq=1 — CTSnake, Apr 25 '17 at 16:22
You can check out https://tex.stackexchange.com/ if you are having trouble typing mathematical symbols. It makes the question look better — Andres Romero, Apr 25 '17 at 20:21

score 3 · Accepted Answer · answered Apr 25 '17 at 18:28

3

I would like to thank @G. Sassatelli for the hint

Here is my try

enter image description here

answered Apr 25 '17 at 18:28

user373141

1 Answers1