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MCQMediumJEE Main 2023 · 30 January, Shift 2Inverse Trigonometric Functions

Mathematics Question from JEE Main 2023 · 30 January, Shift 2

Let a1=1,a2,a3,a4,…a_1 = 1, a_2, a_3, a_4, \dots be consecutive natural numbers. Then

tan⁡−1(11+a1a2)+tan⁡−1(11+a2a3)+⋯+tan⁡−1(11+a2021a2022)\tan^{-1} \left( \frac{1}{1 + a_1 a_2} \right) + \tan^{-1} \left( \frac{1}{1 + a_2 a_3} \right) + \dots + \tan^{-1} \left( \frac{1}{1 + a_{2021}a_{2022}} \right)

is equal to:

  • A

    π4−cot⁡−1(2022)\frac{\pi}{4} - \cot^{-1}(2022)

  • B

    cot⁡−1(2022)−π4\cot^{-1}(2022) - \frac{\pi}{4}

  • C

    tan⁡−1(2022)−π4\tan^{-1}(2022) - \frac{\pi}{4}

  • D

    π4−tan⁡−1(2022)\frac{\pi}{4} - \tan^{-1}(2022)

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