If $\mathop \sum \limits_{i = 1}^{20} {\sin ^{ - 1}}{x_i} = 10\pi ,$ then $\mathop \sum \limits_{i = 1}^{20} {x_i}$ is equal to

JEE MATHEMATICS MCQ: INVERSE TRIGONOMETRY

1 Easy

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Application +4 | -1

\sum \limits_{i = 1}^{20} {\sin ^{ - 1}}{x_i} = 10\pi ,

then

\sum \limits_{i = 1}^{20} {x_i}

is equal to

View answer and explanation

Correct option: A

Option A (20) is correct because the maximum value of

{\sin ^{ - 1}}{x_i}

\frac{\pi }{2}

, and for the sum to be

10\pi

, each term must be

\frac{\pi }{2}

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