$\cos 2^3\large\frac{\pi}{10}$$\cos 2^4\large\frac{\pi}{10}$$\cos 2^5\large\frac{\pi}{10}........$$\cos 2^{10}\large\frac{\pi}{10}$ is equal to

Question

$(a)\;\large\frac{1}{128}$$\qquad(b)\;\large\frac{1}{256}$$\qquad(c)\;\large\frac{1}{512}$$\sin\large\frac{\pi}{10}$$\qquad(d)\;\large\frac{\sqrt 5-1}{512}$$\sin\large\frac{3\pi}{10}$