Mathematics · 2023
JEE Main · 30 January 2023, Shift 2 · Q78
Let a_1=1, a_2, a_3, a_4, ….. be consecutive natural numbers. Then tan^-1(1/(1+a_1 a_2))+ tan^-1(1/(1+a_2 a_3))+…..+ tan^-1(1/(1+a_2021 a_2022)) is…
Let $\displaystyle a_1=1, a_2, a_3, a_4, \ldots$. . be consecutive natural numbers.
Then $\displaystyle \tan ^{-1}\left(\frac{1}{1+a_1 a_2}\right)+\tan ^{-1}\left(\frac{1}{1+a_2 a_3}\right)+\ldots . .+\tan ^{-1}\left(\frac{1}{1+a_{2021} a_{2022}}\right)$ is equal to
Official answer
From NTA’s final answer key for this paper.
(2)
$\displaystyle \frac{\pi}{4}-\cot ^{-1}(2022)$
(4)
$\displaystyle \tan ^{-1}(2022)-\frac{\pi}{4}$
NTA’s answer key accepts either.
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JEE Main 2023 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.