JEE Main 2024MathematicsInverse Trigonometric FunctionsEasyMCQ

JEE Main 2024 — Inverse Trigonometric Functions Question with Solution

JEE Main 2024 (29 Jan Shift 2)

Question

Let x=mn(m,n are co-prime natural numbers) be a solution of the equation cos2sin-1x=19 and let α,β(α>β) be the roots of the equation mx2-nx-m+n=0. Then the point (α,β) lies on the line

Choose an option

Show full solutionCorrect option: D
Correct answer
D5x+8y=9

Step-by-step explanation

Given: cos2sin-1x=19

Let, sin-1x=θ

⇒cos2θ=19

⇒1-2sin2θ=19

⇒89=2sin2θ

⇒sinθ=±23

⇒x=±23

It is given that m and n are co-prime natural numbers,

⇒m=2, n=3

Also, mx2-nx-m+n=0.

⇒2x2-3x-2+3=0

⇒2x2-3x+1=0

⇒2x2-2x-x+1=0

⇒2xx-1-x-1=0

⇒2x-1x-1=0

⇒x=1,12

⇒α=1, β=12

Out of the given options, 1,12 lines on 5x+8y=9.

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About this question

This is a previous-year question from JEE Main 2024, 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.