Trigonometric Identities Question 337
Question: The value of $ \sin \frac{\pi }{14}\sin \frac{3\pi }{14}\sin \frac{5\pi }{14}\sin \frac{7\pi }{14}\sin \frac{9\pi }{14}\sin \frac{11\pi }{14}\sin \frac{13\pi }{14} $ is equal to
[IIT 1991; MNR 1992]
Options:
A) $ \frac{1}{8} $
B) $ \frac{1}{16} $
C) $ \frac{1}{32} $
D) $ \frac{1}{64} $
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Answer:
Correct Answer: D
Solution:
$ \sin \frac{\pi }{14}\sin \frac{3\pi }{14}\sin \frac{5\pi }{14}\sin \frac{7\pi }{14}\sin \frac{9\pi }{14}\sin \frac{11\pi }{14}\sin \frac{13\pi }{14} $ $ =\sin \frac{\pi }{14}\sin \frac{3\pi }{14}\sin \frac{5\pi }{14}\times 1 $ $ \times \sin ( \pi -\frac{5\pi }{14} )\sin ( \pi -\frac{3\pi }{14} )\sin ( \pi -\frac{\pi }{14} ) $ $ ={{[ \sin \frac{\pi }{14}\sin \frac{3\pi }{14}\sin \frac{5\pi }{14}\sin \frac{7\pi }{14} ]}^{2}}=\frac{1}{64} $ .
BETA
