Explanation

(b)
$\cos\frac{\pi}{65}\cos{\frac{2\pi}{65}\ldots\cos{\frac{32\pi}{65} = \cos{\frac{\pi}{65}.\cos{\frac{2\pi}{65}\ldots\cos\frac{2^{5}\pi}{65}}}}}$
$= \frac{\sin\frac{2^{6}\pi}{65}}{2^{6}\sin\frac{\pi}{65}} = \frac{\sin\frac{65\pi}{65}}{64\sin\frac{\pi}{65}}$
$= \frac{\sin\left( \pi - \frac{\pi}{65} \right)}{64\sin\frac{\pi}{65}} = \frac{1}{64}$