JEE Main 2022MathematicsInverse Trigonometric FunctionsHardMCQ

JEE Main 2022 — Inverse Trigonometric Functions Question with Solution

JEE Main 2022 (24 Jun Shift 1)

Question

The set of all values of k for which tan-1x3+cot-1x3=kπ3,x∈R, is the interval

Choose an option

Show full solutionCorrect option: A
Correct answer
A132,78

Step-by-step explanation

Let T=tan-1x3+cot-1x3

=tan-1x+cot-1x3-3tan-1x·cot-1xtan-1x+cot-1x

=π38-3π2tan-1xπ2-tan-1x ∵tan-1x+cot-1x=π2

=3π2tan-1x2-3π24tan-1x+π38

T=3π2tan-1x-π42+π332

We know than tan-1x∈-π2,π2

Minimum value of T is at tan-1x=π4 and maximum value at tan-1x=-π2

⇒π332≤T<78π3

=π332≤kπ3<78π3

⇒132≤k<78

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About this question

This is a previous-year question from JEE Main 2022, 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.