Q. If $\sum_{i = 1}^{20}{\sin^{- 1}{x_{i} = 10\pi,}}$then $\sum_{i = 1}^{20}x_{i}$ is equal to
A) 20
B) 10
C) 0
D) None of these
Explanation
(a)
Since, $- \frac{\pi}{2} < \sin^{- 1}{x \leq \frac{\pi}{2}}$
$\therefore\sin^{- 1}{x_{i} = \frac{\pi}{2},1 \leq i \leq 20}$
$\Rightarrow x_{i} = 1,\ 1 \leq i \leq 20$
Thus, $\sum_{i = 1}^{20}{x_{i} = 20}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.