JEE Advanced 2018 Mathematics question

MathematicsInverse Trigonometric FunctionsJEE Advanced 2018

For any positive integer , define as

=() for all x(0,∞).

(Here, the inverse trigonometric function assumes values in .) Then, which of the following statement(s) is (are) TRUE?

Answer: (D)

Solution

, so the sum telescopes: . (A), (B) Each is defined only on , so and are not defined and these

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Question ID VK-026790