JEE Main 2019MathematicsTrigonometric EquationsEasyMCQ

JEE Main 2019 — Trigonometric Equations Question with Solution

JEE Main 2019 (12 Apr Shift 1)

Question

The number of solutions of the equation 1+sin4x=cos23x, x∈-5π2,5π2 is:

Choose an option

Show full solutionCorrect option: A
Correct answer
A5

Step-by-step explanation

The given trigonometric equation can be written as
1-cos23x+sin4x=0

⇒ sin23x+sin4x=0

⇒sin3x=0 and sinx=0 , x∈-5π2,5π2 

In given interval sinx=0 at x=-2π, -π, 0, π, 2π and these values are also satisfied by sin3x=0.
Hence total number of solutions is 5.

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About this question

This is a previous-year question from JEE Main 2019, 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.