Limit with cos and fraction I have been asked to find:
$\lim_{x\to 0} \, \cos \left(\frac{\pi -\pi  \cos ^2(x)}{x^2}\right)$$=-1$
Without using l'Hôpital's rule. But I have no idea how to due it, could someone show a step by step process all the way to the answer? 

Hint: We have 
$$\frac{\pi -\pi\cos^2 x}{x^2}=\frac{\pi\sin^2 x}{x^2}=\pi \left(\frac{\sin x}{x}\right)^2.$$
