Question

The value of the expression $\cos \frac{\pi }{33}\cos \frac{2\pi }{33}\cos \frac{4\pi }{33}\cos \frac{8\pi }{33}\cos \frac{11\pi }{33}\cos \frac{16\pi }{33}$ is

• A. $\frac{1}{64}$
• B. $-\frac{1}{32}$
• C. $\frac{1}{32}$
• D. $\frac{31}{64}$

Answer 1

The correct option is A $\frac{1}{64}$

$\cos \frac{\pi }{33}\cos \frac{2\pi }{33}\cos \frac{4\pi }{33}\cos \frac{8\pi }{33}\cos \frac{11\pi }{33}\cos \frac{16\pi }{33}$
$\Rightarrow \cos \frac{\pi }{33}\cos \frac{2\pi }{33}\cos \frac{4\pi }{33}\cos \frac{8\pi }{33}\cos \frac{16\pi }{33}\cos \frac{11\pi }{33}$
$\Rightarrow \frac{1}{2}\frac{\sin (2^5.\frac{\pi }{33})}{2^5\sin \frac{\pi }{33}}=\frac{1}{64}$