Question

The value of
$\cos \left(\pi /5\right)\cos \left(2\pi /5\right)\cos \left(4\pi /5\right)\cos \left(8\pi /5\right)$ is

• A. $\frac{1}{16}$
• B. $0$
• C. $\frac{-1}{8}$
• D. $\frac{-1}{16}$

Answer 1

The correct option is D $\frac{-1}{16}$

$\cos \left(\pi /5\right)\cos \left(2\pi /5\right)\cos \left(4\pi /5\right)\cos \left(8\pi /5\right)=\frac{1}{2^4\sin \left(\pi /5\right)}\sin \frac{2^4\pi }{5}$
$=-\frac{1}{16}[\because \sin \frac{16\pi }{5}=\sin (3\pi +\frac{\pi }{5})=-\sin \frac{\pi }{5}]$