First slide

Introduction to ITF

Question

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

Moderate

A

20
B

10
C

0
D

None of these

Solution

$Since, - \frac{π}{2} < \sin^{- 1} x \leq \frac{π}{2} \sin^{- 1} x_{1} + \sin^{- 1} x_{2} + \dots + \sin^{- 1} x_{20} = 10 π \sin^{- 1} x_{i} contains maximum value i.e. (\frac{π}{2}) . \begin{array}{l} ∴ \sin^{- 1} x_{i} = \frac{π}{2}, 1 \leq i \leq 20 \\ \Rightarrow x_{i} = 1, 1 \leq i \leq 20 \\ Thus, \sum_{i = 1}^{20} x_{i} = 20 \end{array}$

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