Q. If $a = \frac{\pi}{18}$ rad, then $\cos{a + \cos{2a + ... + \cos{18a}}}$ is equal to
A) 0
B) $- 1$
C) 1
D) $\pm 1$
Explanation
(b)
$\cos{\frac{\pi}{18} + \cos{\frac{2\pi}{18} + ... + \cos{\frac{16\pi}{18} + \cos{\frac{17\pi}{18} + \cos\pi}}}}$
$= \cos{\frac{\pi}{18} + \cos{\frac{2\pi}{18} + ... - \cos{\frac{2\pi}{18} - \cos{\frac{\pi}{18} + \cos\pi}}}}$
$= \cos{\pi = - 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.