$\lim\limits_{x\to \infty}\cos(\large\frac{x}{2})$$\cos(\large\frac{x}{4})$$\cos(\large\frac{x}{8})$$........\cos(\large\frac{x}{2^n})$ is

Question

$\begin{array}{1 1}(a)\;1&(b)\;\large\frac{\sin x}{x}\\(c)\;\large\frac{x}{\sin x}&(d)\;\text{None of these}\end{array}$