A) 0
B) \[-1\]
C) 1
D) \[\pm 1\]
E) none of these
Correct Answer: B
Solution :
\[\cos a+\cos 2a+....+\cos 18a\] \[=\cos \frac{\pi }{18}+\cos \frac{\pi }{18}+.....\] \[+\cos \frac{16\pi }{18}+\cos \frac{17\pi }{18}+\cos \pi \] \[=\cos \frac{\pi }{18}+\cos \frac{2\pi }{18}+....\] \[-\cos \frac{2\pi }{18}-\cos \frac{\pi }{18}+\cos \pi \] \[=\cos \pi \] \[=-1\]
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