JEE Main 2023MathematicsInverse Trigonometric FunctionsMediumNumerical

JEE Main 2023 — Inverse Trigonometric Functions Question with Solution

JEE Main 2023 (13 Apr Shift 2)

Question

For x∈(-1,1], the number of solutions of the equation sin-1x=2tan-1x is equal to

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Show full solutionCorrect answer: 2
Correct answer
2

Step-by-step explanation

Given that sin-1x=2tan-1x

⇒sin-1x=sin-12x1+x2

⇒x=2x1+x2

⇒x+x3=2x

⇒x3-x=0

⇒x(x2-1)=0

⇒x=0,-1,1.

But x∈(-1,1], so the number of roots are 2, x=0 & 1

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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.