JEE Main 2023MathematicsInverse Trigonometric FunctionsHardNumerical

JEE Main 2023 — Inverse Trigonometric Functions Question with Solution

JEE Main 2023 (25 Jan Shift 1)

Question

If the sum of all the solutions of
tan-12x1-x2+cot-11-x22x=π3, -1<x<1,x≠0, is α-43, then α is equal to _____ .

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Show full solutionCorrect answer: 2
Correct answer
2

Step-by-step explanation

Given,

tan-12x1-x2+cot-11-x22x=π3 where x∈-1,1

Case 1: When x<0, then

tan-12x1-x2+cot-11-x22x=π3

⇒2tan-1x+π+2tan-1x=π3

⇒4tan-1x=-π+π3

⇒4tan-1x=-2π3

⇒tan-1x=-π6

⇒x=-13

Case 2: When x≥0,

tan-12x1-x2+cot-11-x22x=π3

⇒2tan-1x+2tan-1x=π3

⇒tan-1x=π12

⇒x=2-3

So, sum of solution will be 

-13+2-3=2-43

Now, on comparing with α-43, we get

α=2 

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About this question

This is a previous-year question from JEE Main 2023, 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.