If ∑$$i=120$$ $$sin$$−$$1$$⁡$$xi=10$$π then ∑$$i=120$$ xi is equal to

Since −π$$2$$≤$$sin$$$$-1xi$$≤π$$2$$,∴$$sin$$−$$1$$⁡$$xi=$$π$$2$$,$$1$$≤i≤$$20$$ ∴$$xi=1$$,$$1$$≤i≤$$20$$. Thus, ∑$$i=120$$ $$xi=20$$.

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$If \sum_{i = 1}^{20} \sin^{- 1} x_{i} = 10 π then \sum_{i = 1}^{20} x_{i}$ is equal to

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$Since - \frac{π}{2} \leq \sin^{- 1} x_{i} \leq \frac{π}{2}, ∴ \sin^{- 1} x_{i} = \frac{π}{2}, 1 \leq i \leq 20 ∴ x_{i} = 1, 1 \leq i \leq 20 . Thus, \sum_{i = 1}^{20} x_{i} = 20 .$

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