JEE Main 2022MathematicsTrigonometric EquationsMediumMCQ

JEE Main 2022 — Trigonometric Equations Question with Solution

JEE Main 2022 (24 Jun Shift 2)

Question

The number of solutions of the equation cosx+π3cosπ3-x=14cos22x, x∈-3π,3π is:

Choose an option

Show full solutionCorrect option: D
Correct answer
D7

Step-by-step explanation

Given,

cosx+π3cosx-π3=14cos22x

⇒2cosx+π3cosx-π3=12cos22x

⇒cos2x+cos2π3=12cos22x

⇒cos2x+-12=12cos22x

⇒cos22x-2cos2x+1=0

⇒cos2x-12=0 or  cos2x=1

⇒2x=-6π,-4π,-2π,0,2π,4π,6π

So, x∈-3π,-2π,-π,0,π,2π,3π

So total 7 solutions.

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About this question

This is a previous-year question from JEE Main 2022, 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.