JEE Main 2024MathematicsTrigonometric Ratios & IdentitiesMediumMCQ

JEE Main 2024 — Trigonometric Ratios & Identities Question with Solution

JEE Main 2024 (30 Jan Shift 2)

Question

For α,β∈0,π2 let 3sin(α+β)=2sin(α-β) and a real number k be such that tanα= tanβ. Then the value of k is equal to

Choose an option

Show full solutionCorrect option: A
Correct answer
A-5

Step-by-step explanation

Given:

 3sinα+β=2sinα-β

⇒sinα+βsinα-β=23

⇒sinα+β+sinα-βsinα+β-sinα-β=2+32-3

⇒2sinαcosβ2cosαsinβ=-5

⇒tanαtanβ=-5

⇒tanα=-5tanβ

⇒k=-5

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About this question

This is a previous-year question from JEE Main 2024, covering the Trigonometric Ratios & Identities 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.