JEE Main 2021MathematicsTrigonometric EquationsEasyMCQ

JEE Main 2021 — Trigonometric Equations Question with Solution

JEE Main 2021 (16 Mar Shift 1)

Question

The number of roots of the equation, 81sin2x+81cos2x=30 in the interval 0,π is equal to :

Choose an option

Show full solutionCorrect option: B
Correct answer
B4

Step-by-step explanation

81sin2x+81cos2x=30

81sin2x+81181sin2x=30

81sin2x=t

t+81t=30

t2-30t+81=0

t-3t-27=0

81sin2x=31 or  81sin2x=33

34sin2x=31  or   34sin2x=33

sin2x=14  or  sin2x=34

  

Hence, total 4 solution.

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About this question

This is a previous-year question from JEE Main 2021, 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.