JEE Main 2023MathematicsTrigonometric EquationsMediumNumerical

JEE Main 2023 — Trigonometric Equations Question with Solution

JEE Main 2023 (25 Jan Shift 2)

Question

If m and n respectively are the numbers of positive and negative value of θ in the interval -π,π that satisfy the equation cos2θcosθ2=cos3θcos9θ2, then mn is equal to _____ .

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Show full solutionCorrect answer: 25
Correct answer
25

Step-by-step explanation

We have,

cos2θ·cosθ2=cos3θ·cos9θ2

⇒2cos2θcosθ2=2cos9θ2cos3θ

⇒ cos5θ2+cos3θ2=cos15θ2+cos3θ2

⇒cos15θ2=cos5θ2

⇒15θ2=2kπ±5θ2; k∈Z

⇒5θ=2kπ or 10θ=2kπ

⇒θ=2kπ5 or θ=kπ5

∴θ=-π,-4π5,-3π5,-2π5,-π5,0,π5,2π5,3π5,4π5,π

So, m=5,n=5

∴ mn=25.

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About this question

This is a previous-year question from JEE Main 2023, 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.