JEE Main 2022MathematicsTrigonometric EquationsMediumNumerical

JEE Main 2022 — Trigonometric Equations Question with Solution

JEE Main 2022 (25 Jun Shift 1)

Question

The number of values of x in the interval π4,7π4 for which 14cosec2x-2sin2x=21-4cos2x holds, is ______.

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Show full solutionCorrect answer: 4
Correct answer
4

Step-by-step explanation

Given x∈π4,7π4

14cosec2x-2sin2x=21-4cos2x

=21-41-sin2x

=17+4sin2x

14sin2x-6sin2x=17

Let sin2x=p

14p-6p=17⇒14-6p2=17p

6p2+17p-14=0

p=-72,23⇒sin2x=23

⇒sinx=±23

∴  There are 4 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.