JEE Main 2023MathematicsTrigonometric EquationsMediumMCQ

JEE Main 2023 — Trigonometric Equations Question with Solution

JEE Main 2023 (29 Jan Shift 2)

Question

The set of all values of λ for which the equation cos22x-2sin4x-2cos2x=λ

Choose an option

Show full solutionCorrect option: D
Correct answer
D-32,-1

Step-by-step explanation

Given:

λ=cos22x-2sin4x-2cos2x

⇒λ=2cos2x-12-21-cos2x2-2cos2x

⇒λ=4cos4x-4cos2x+1-21-2cos2x+cos4x-2cos2x

⇒λ=2cos4x-2cos2x+1-2

⇒λ=2cos4x-2cos2x-1

⇒λ=2cos4x-cos2x-12

⇒λ=2cos2x-122-34

So,

λmax=214-34=-1  (max Value)

λmin=20-34=-32  (Minimum Value)

So, range of λ is-32,-1

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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.