Trigonometric Identities Question 42
Question: The expression $ 2\cos \frac{\pi }{13}.\cos \frac{9\pi }{13}+\cos \frac{3\pi }{13}+\cos \frac{5\pi }{13} $ is equal to
[UPSEAT 2004]
Options:
A) -1
B) 0
C) 1
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ 2\cos \frac{\pi }{13}.\cos \frac{9\pi }{13}+\cos \frac{3\pi }{13}+\cos \frac{5\pi }{13} $ $ =2\cos \frac{\pi }{13}.\cos \frac{9\pi }{13}+2\cos \frac{4\pi }{13}\cos \frac{\pi }{13} $ $ =2\cos \frac{\pi }{13}[ \cos \frac{9\pi }{13}+\cos \frac{4\pi }{13} ] $ $ =2\cos \frac{\pi }{13}[ 2\cos \frac{\pi }{2}.\cos \frac{5\pi }{26} ]=0 $ , $ [ \because \cos \frac{\pi }{2}=0 ] $ .
BETA
