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+1 vote
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The value of \(tan^{-1} \left(\frac 1{1 + a_1a_2}\right) + \tan^{-1} \left(\frac 1{1 + a_2a_3}\right) + ....+ \tan^{-1} \left(\frac 1{1 + a_{2021}a_{20222}}\right)\) if a1 = 1 and ai are consecutive natural numbers

(1) \(\frac \pi4 - \cot^{-1} (2021)\)

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

(3) \(\frac \pi4 - \tan^{-1} (2021)\)

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

1 Answer

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by (54.9k points)
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Best answer

Correct option is (2) \(\frac \pi 4 - \cot^{-1} (2022)\)

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