The sum of all values of $x$ in $[0,2\pi]$, for which $\sin x+\sin2x+\sin3x+\sin4x=0$, is equal to :

JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 25 July 2021, Shift 1, Maths Q80

Question 80 of 90 in this shift, Maths question 20 of 30, Section A.

The sum of all values of

x

[0,2\pi]

, for which

\sin x+\sin2x+\sin3x+\sin4x=0

, is equal to :

(1) $8\pi$
(2) $9\pi$ Official answer
(3) $11\pi$
(4) $12\pi$

Official answer

Option 2

NTA final key.

Chapter: Trigonometric Functions
Topic: General Solutions
Idea tested: Sum-to-Product Factorization

Same topic in other shifts

All General Solutions questions

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Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.