Explanation

(d)
$\cos{\frac{\pi}{5}\cos{\frac{2\pi}{5}\cos{\frac{4\pi}{5}\cos{\frac{8\pi}{5} = \frac{\sin{2^{4}\frac{\pi}{5}}}{2^{4}\sin\frac{\pi}{5}}}}}}\ \left( \because\cos{x\cos{2x\cos{4x\ldots\cos{2nx = \frac{\sin{2^{n}x}}{2^{n}\sin x}}}}} \right)$
$= \frac{\sin\frac{16\pi}{5}}{16\sin\frac{\pi}{5}} = \frac{\sin\left( 3\pi + \frac{\pi}{5} \right)}{16\sin\frac{\pi}{5}}$
$= \frac{- \sin\frac{\pi}{5}}{16\sin\frac{\pi}{5}} = - \frac{1}{16}$