JEE Main 2022MathematicsTrigonometric EquationsEasyNumerical

JEE Main 2022 — Trigonometric Equations Question with Solution

JEE Main 2022 (29 Jun Shift 1)

Question

The number of elements in the set S=θ∈-4π,4π: 3cos22θ+6cos2θ-10cos2θ+5=0 is ______.

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Show full solutionCorrect answer: 32
Correct answer
32

Step-by-step explanation

3cos22θ+6cos2θ-10cos2θ+5=0

3cos22θ+6cos2θ-51+cos2θ+5=0

cos2θ3cos2θ+1=0

cos2θ=0 or cos2θ=-13

Given θ∈-4π,4π⇒2θ∈-8π,8π

So for 2θ=2n+1π2

 θ=±π4,±3π4,………±15π4 gives 16 solution

Similarly cos2θ=-13 gives 16 solution

hence, total elements in set S will be 32

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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.