JEE Main 2021MathematicsInverse Trigonometric FunctionsHardMCQ

JEE Main 2021 — Inverse Trigonometric Functions Question with Solution

JEE Main 2021 (17 Mar Shift 1)

Question

If cot-1(α)=cot-12+cot-18+cot-118+cot-132+…. upto 100 terms, then α is:

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Show full solutionCorrect option: A
Correct answer
A1.01

Step-by-step explanation

Given cot-1(α)=cot-1(2)+cot-1(8)+cot-1(18)+….

=∑n=1100tan-124n2

=∑n=1100tan-1(2n+1)-(2n-1)1+(2n+1)(2n-1)

=∑n=1100tan-12n+1-tan-12n-1

=tan-1201-tan-11

=tan-1200202

∴cot-1(α)=cot-1202200

α=1.01

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About this question

This is a previous-year question from JEE Main 2021, covering the Inverse Trigonometric Functions chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.