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Q.
If $\displaystyle\sum_{i=1}^{20} \sin ^{-1} x_{i}=10 \pi$ then find the value of $\displaystyle\sum_{i=1}^{20} x_{i}$.
Inverse Trigonometric Functions
Solution:
$\frac{-\pi}{2} \leq \sin ^{-1} x _{ i } \leq \frac{\lambda}{2} $
$ \because \sin ^{-1} x _{ i }=\frac{\pi}{2}$
$x _{ i }=1 $
$ \because 1 \leq i \leq 20$
so, $\displaystyle\sum_{i=1}^{20} x_{i}=20$