Trigonometric Identities Question 88
Question: $ \cos \frac{2\pi }{15}\cos \frac{4\pi }{15}\cos \frac{8\pi }{15}\cos \frac{16\pi }{15} $ =
[IIT 1985]
Options:
A) 1/2
B) 1/4
C) 1/8
D) 1/16
Show Answer
Answer:
Correct Answer: D
Solution:
$ \cos \frac{2\pi }{15}\cos \frac{4\pi }{15}\cos \frac{8\pi }{15}\cos \frac{16\pi }{15} $ $ =\frac{\sin ,2^{4}\frac{2\pi }{15}}{2^{4}\sin \frac{2\pi }{15}}=\frac{\sin ,\frac{32\pi }{15}}{16,\sin \frac{2\pi }{15}}=\frac{1}{16}\frac{\sin \frac{2\pi }{15}}{\sin \frac{2\pi }{15}}=\frac{1}{16} $ .
BETA
