Question

The value of $\sin \frac{\pi }{14}\sin \frac{3\pi }{14}\sin \frac{5\pi }{14}$ is :-

• A. $\frac{1}{16}$
• B. $\frac{1}{8}$
• C. $\frac{1}{2}$
• D. 1

Answer 1

Answer: (B)

$\frac{1}{8}$

The value of $\sin \frac{\pi }{14}\sin \frac{3\pi }{14}\sin \frac{5\pi }{14}$
$=\cos (\frac{\pi }{2}-\frac{\pi }{14})\cos (\frac{\pi }{2}-\frac{3\pi }{14})\cos (\frac{\pi }{2}-\frac{5\pi }{14})$
$=\cos \frac{3\pi }{7}\cos \frac{2\pi }{7}\cos \frac{4\pi }{7}$
$=-\frac{\sin 2^3\frac{\pi }{7}}{2^3\sin \frac{\pi }{7}}=-\frac{1}{8}\frac{\sin \frac{8\pi }{7}}{\sin \frac{\pi }{7}}=-\frac{1}{8}$