A) -1
B) 0
C) 1
D) None of these
Correct Answer: B
Solution :
\[2\cos \frac{\pi }{13}.\cos \frac{9\pi }{13}+\cos \frac{3\pi }{13}+\cos \frac{5\pi }{13}\] \[=2\cos \frac{\pi }{13}.\cos \frac{9\pi }{13}+2\cos \frac{4\pi }{13}\cos \frac{\pi }{13}\] \[=2\cos \frac{\pi }{13}\left[ \cos \frac{9\pi }{13}+\cos \frac{4\pi }{13} \right]\] \[=2\cos \frac{\pi }{13}\left[ 2\cos \frac{\pi }{2}.\cos \frac{5\pi }{26} \right]=0\], \[\left[ \because \cos \frac{\pi }{2}=0 \right]\].
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