How can I calculate $\displaystyle\lim_{x \to \infty}x^{2}\ln\left(\cos \left(\pi/x\right)\right) $? Does anybody know how to solve this?
$$\lim_{x \to \infty}x^{2}\ln\left(\cos\left(\pi \over x\right)\right)$$ 

An entirely different approach is to reexpess $x^2 \ln{\big(\cos{(\frac{\pi}{x})}\big)}$ as  $\ln{\big(\big(\cos{(\frac{\pi}{x}})\big)^{x^2}\big)}$.
