JEE Main 2021MathematicsTrigonometric EquationsMediumMCQ

JEE Main 2021 — Trigonometric Equations Question with Solution

JEE Main 2021 (25 Jul Shift 1)

Question

The sum of all values of x in [0,2π], for which sinx+sin2x+sin3x+sin4x=0, is equal to :

Choose an option

Show full solutionCorrect option: D
Correct answer
D9π

Step-by-step explanation

Given,

sinx+sin2x+sin3x+sin4x=0

⇒(sinx+sin4x)+(sin2x+sin3x)=0

⇒2sin5x2cos3x2+2sin5x2cosx2=0

⇒2sin5x2cos3x2+cosx2=0

⇒2sin5x22cosxcosx2=0

2sin5x2=0⇒5x2=0,π,2π,3π,4π,5π

⇒x=0,2π5,4π5,6π5,8π5,2π

and cosx2=0⇒x2=π2⇒x=π

and cosx=0⇒x=π2,3π2

So sum =6π+π+2π=9π

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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.