JEE Main 2023 (Online) 30th January Evening Shift

MCQ (More than One Correct Answer)

-1

Let $a_{1}=1, a_{2}, a_{3}, a_{4}, \ldots .$. be consecutive natural numbers.

Then $\tan ^{-1}\left(\frac{1}{1+a_{1} a_{2}}\right)+\tan ^{-1}\left(\frac{1}{1+a_{2} a_{3}}\right)+\ldots . .+\tan ^{-1}\left(\frac{1}{1+a_{2021} a_{2022}}\right)$ is equal to :

$\frac{\pi}{4}-\cot ^{-1}(2022)$

$\frac{\pi}{4}-\tan ^{-1}(2022)$

$\cot ^{-1}(2022)-\frac{\pi}{4}$

$\tan ^{-1}(2022)-\frac{\pi}{4}$

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