JEE Main 2023MathematicsInverse Trigonometric FunctionsMediumMCQ

JEE Main 2023 — Inverse Trigonometric Functions Question with Solution

JEE Main 2023 (01 Feb Shift 2)

Question

Let S=x∈R:0<x<1 and 2tan-11-x1+x=cos-11-x21+x2. If n(S) denotes the number of elements in S then :

Choose an option

Show full solutionCorrect option: C
Correct answer
Cn(S)=1 and the element in S is less then 12

Step-by-step explanation

Given, 0<x<1

2tan-11-x1+x=cos-11-x21+x2

Put x=tanθ    ; 0<θ<π4

2tan-11-tan θ1+tan θ=cos-11-tan2θ1+tan2θ

⇒2tan-1tanπ4-θ=cos-1(cos2θ)

2π4-θ=2θ⇒θ=π8

Put θ=tan-1x we get,

x=tanπ8∴x=2-1≃0.414<12

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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.