Trigonometric Identities Question 50
Question: $ \cos \frac{\pi }{5}\cos \frac{2\pi }{5}\cos \frac{4\pi }{5}\cos \frac{8\pi }{5}= $
Options:
A) 1/16
B) 0
C) - 1/8
D) -1/16
Show Answer
Answer:
Correct Answer: D
Solution:
$ \cos \frac{\pi }{5}\cos \frac{2\pi }{5}\cos \frac{4\pi }{5}\cos \frac{8\pi }{5} $ $ =\frac{\sin \frac{2^{4}\pi }{5}}{2^{4}\sin \frac{\pi }{5}}=\frac{\sin \frac{16\pi }{5}}{16,\sin \frac{\pi }{5}}=\frac{\sin ,( 3\pi +\frac{\pi }{5} )}{16,\sin \frac{\pi }{5}} $ $ =\frac{-\sin \frac{\pi }{5}}{16,\sin \frac{\pi }{5}}=-\frac{1}{16} $ .
BETA
