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Let \({a}_{1}=1,{a}_{2},{a}_{3},{a}_{4},\ldots .\). be consecutive natural numbers. Then \({\tan }^{-1}\left(\frac{1}{1+…

Q1

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

[JEE Main 2023, 30 Jan (Shift 2)]

a

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

b

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

c

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

d

None of these

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