JEE Main 2024MathematicsTrigonometric EquationsEasyMCQ

JEE Main 2024 — Trigonometric Equations Question with Solution

JEE Main 2024 (01 Feb Shift 2)

Question

The number of solutions of the equation 4sin2x−4cos3x+9−4cosx=0;x∈−2π,2π is:

Choose an option

Show full solutionCorrect option: D
Correct answer
D0

Step-by-step explanation

Given: 4sin2x-4cos3x+9-4cosx=0

⇒4-4cos2x-4cos3x+9-4cosx=0

⇒4cos3x+4cos2x+4cosx-13=0

⇒4cos3x+4cos2x+4cosx=13

We know that, -1≤cosx≤1

So, the maximum value of LHS is 4+4+4=12

But, RHS is 13.

So, no solutions are possible for the given equation.

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Trigonometric Equations chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

About this question

This is a previous-year question from JEE Main 2024, 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.