Question

Value of $\cos \frac{\pi }{33}\cos \frac{2\pi }{33}\cos \frac{4\pi }{33}\cos \frac{8\pi }{33}\cos \frac{16\pi }{33}$

• A. $1/16$
• B. $1/32$
• C. $1/64$
• D. $-1/16$

Answer 1

Answer: (B)

$\frac{\sin \frac{2^5\pi }{33}}{2^5\sin \frac{\pi }{33}}=\frac{\sin \frac{32\pi }{33}}{32\sin \frac{\pi }{33}}=\frac{\sin \left(\pi -\frac{\pi }{33}\right)}{32\sin \frac{\pi }{33}}=\frac{\sin \frac{\pi }{33}}{32\sin \frac{\pi }{33}}=\frac{1}{32}$