The sum of the solutions in (0,2 π) the equation x ((π)/(3)-x) ((π)/(3)+x)=(1)/(4) is

Correct answer: C. 2 π We know, x ((π)/(3)- x) ((π)/(3)+ x)= (1)/(4) 3 θ But it is given aligned & x ((π)/(3)-x) ((π)/(3)+x)=(1)/(4) 3 θ& =1 3 θ& =2 π,4 π θ& =(2 π)/(3), (4 π)/(3) aligned Sum of solutions aligned & =(2 π)/(3)+(4 π)/(3)=(6 π)/(3) & =2 π aligned

JEE Main

Exam: JEE Main
Subject: Mathematics
Chapter: Trigonometric Ratios & Identities

JEE Main · Mathematics · Trigonometric Ratios & Identities

The sum of the solutions in (0,2 π) the equation x ((π)/(3)-x)...

The sum of the solutions in

(0,2 \pi)

the equation

\cos x \cos

\left(\frac{\pi}{3}-x\right) \cos

\left(\frac{\pi}{3}+x\right)=\frac{1}{4}

Options

A $4 \pi$
B $\pi$
C $2 \pi$
D $3 \pi$

Correct answer

C. $2 \pi$

Step-by-step solution

We know, \cos x \cos \left(\frac{\pi}{3}-

x\right) \cos \left(\frac{\pi}{3}+

x\right)=

\frac{1}{4} \cos

\theta

But it is given

\begin{aligned}& \cos x \cos \left(\frac{\pi}{3}-x\right) \cos \left(\frac{\pi}{3}+x\right)=\frac{1}{4}\\ \therefore \quad \cos 3 \theta& =1 \\ \Rightarrow \quad 3 \theta& =2 \pi,4 \pi\\ \Rightarrow \quad \theta& =\frac{2 \pi}{3}, \frac{4 \pi}{3} \end{aligned}

\therefore

Sum of solutions

\begin{aligned}& =\frac{2 \pi}{3}+\frac{4 \pi}{3}=\frac{6 \pi}{3}\\ & =2 \pi \end{aligned}

Practice Trigonometric Ratios & Identities on Quantrex Academy →

More from Trigonometric Ratios & Identities

Let α = (1 - 2 ((π)/(11)))(1 - 2 ((3π)/(11)))(1 - 2 ((9π)/(11)))(1 - 2 ((27π)/(11)))(1… JEE Advanced 2026 If A = ( 3^∘)/( 9^∘) + ( 9^∘)/( 27^∘) + ( 27^∘)/( 81^∘) and B = 81^∘ - 3^∘ , then (B)/(A)… JEE Main 2026 Let P = \ θ ∈ [0, 4π] : ^2θ ≠ 1\ and S = \ a ∈ ℤ : 2( ^8θ - ^8θ) 2θ = a^2, θ ∈ P\ . Then… JEE Main 2026 If ((π)/(18)) ((5π)/(18)) ((7π)/(18)) = K , then the value of ((10Kπ)/(3)) is : JEE Main 2026 If (A-B) A + ^ 2 C ^ 2 ~A =1, ~A, ~B, C ∈(0, (π)/(2)) , then JEE Main 2026 If x=(5)/(12) for some x ∈(π, (3 π)/(2)) , then 7 x( (13 x)/(2)+ (13 x)/(2))+ 7 x( (13… JEE Main 2026 The value of 3 cosec 20^ ∘ - 20^ ∘ 20^ ∘ 40^ ∘ 60^ ∘ 80^ ∘ is equal to JEE Main 2026 The least value of ( ^ 2 θ-6 θ θ+3 ^ 2 θ+2) is JEE Main 2026 Let (π)/(2) ((15 θ)/(2))( 8 θ+ 8 θ)+ ((15 θ)/(2))( 8 θ- 8 θ) is equal to JEE Main 2026 Let α and β respectively be the maximum and the minimum values of the function f(θ)=4( ^… JEE Main 2026 Let (α+β)=-(1)/(10) and (α-β)=(3)/(8) , where 0<α<(π)/(3) and 0<β<(π)/(4) . If 2 α= 3(1-r… JEE Main 2026 If ^ 2 48^ ∘ - ^ 2 12^ ∘ ^ 2 24^ ∘ - ^ 2 6^ ∘ = α+β 5 2 , where α, β ∈ ℕ , then α+β is… JEE Main 2026 The value of cosec 10^ ∘ - 3 10^ ∘ is equal to : JEE Main 2026 Let α= 1 60^ ∘ 61^ ∘ + 1 62^ ∘ 63^ ∘ +…+ 1 118^ ∘ 119^ ∘ Then the value of ( cosec 1^ ∘ α… JEE Advanced 2025 If x+ ^2 x=1, x ∈(0, (π)/(2)) , then ( ^ 12 x+ ^ 12 x)+3( ^ 10 x+ ^ 10 x+ ^8 x+ ^8 x)+(… JEE Main 2025 If ∑_ r=1 ^ 13 \ (1)/( ((π)/(4)+(r-1) (π)/(6)) ((π)/(4)+(r π)/(6)))\ =a 3 +b, a, b ∈ Z… JEE Main 2025 Full Trigonometric Ratios & Identities list Trigonometric Ratios & Identities JEE Maths PYQs JEE Mathematics PYQs All 99 Percentile Qs Bank for JEE Main PYQs