Question

$\cos \frac{\pi }{7}\cos \frac{2\pi }{7}\cos \frac{4\pi }{7}=?$

• A. $0$
• B. $\frac{1}{2}$
• C. $\frac{1}{3}$
• D. $-\frac{1}{8}$

Answer 1

The correct option is D $-\frac{1}{8}$

Given

$\cos \frac{\pi }{7}\cos \frac{2\pi }{7}\cos \frac{4\pi }{7}$

Mulitply and Divide by $2\sin \frac{\pi }{7}$

$⟹\frac{1}{2\sin \frac{\pi }{7}}\times 2\sin \frac{\pi }{7}\cos \frac{\pi }{7}\cos \frac{2\pi }{7}\cos \frac{4\pi }{7}$

$⟹\frac{1}{2\sin \frac{\pi }{7}}\times \sin \frac{2\pi }{7}\cos \frac{2\pi }{7}\cos \frac{4\pi }{7}$

$⟹\frac{1}{4\sin \frac{\pi }{7}}\times \sin \frac{4\pi }{7}\cos \frac{4\pi }{7}$

$⟹\frac{1}{8\sin \frac{\pi }{7}}\times \sin \frac{8\pi }{7}$

$⟹-\frac{\sin \frac{\pi }{7}}{8\sin \frac{\pi }{7}}$

$⟹-\frac{1}{8}$