JEE Main 2024MathematicsTrigonometric EquationsMediumMCQ

JEE Main 2024 — Trigonometric Equations Question with Solution

JEE Main 2024 (29 Jan Shift 1)

Question

If α,-π2<α<π2 is the solution of 4cosθ+5sinθ=1, then the value of tanα is

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Show full solutionCorrect option: C
Correct answer
C10-1012

Step-by-step explanation

Given: 4cosθ+5sinθ=1

⇒41-tan2θ21+tan2θ2+52tanθ21+tan2θ2=1

⇒5tan2θ2-10tanθ2-3=0

⇒tanθ2=10±100-45-32×5

⇒tanθ2=10±16010

⇒tanθ2=5±405

It is given that, α∈-π2,π2

⇒α2∈-π4,π4

⇒tanα2∈-1,1

⇒tanα2=5-405

We know that, tanθ=2tanθ21-tan2θ2

⇒tanα=25-4051-5-4052

⇒tanα=25-4052405-85

⇒tanα=5-4040-4

⇒tanα=40-2024

⇒tanα=10-1012

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About this question

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