How to evaluate $\lim\limits_{n\to \infty}\prod\limits_{r=2}^{n}\cos\left(\frac{\pi}{2^{r}}\right)$ How do I evaluate this limit ?
$$\lim_{n\to \infty}\cos\left(\frac{\pi}{2^{2}}\right)\cos\left(\frac{\pi}{2^{3}}\right)\cdots\cos\left(\frac{\pi}{2^{n}}\right)$$
I assumed it is using this formaula $\displaystyle \cos(A)=\sqrt{\frac{1+\cos(2A)}{2}}$ But I am stuck

Hint: $\cos x = \dfrac{\sin (2x)}{2\sin x}$
