Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Trigonometric Equations

NTA Abhyas 2020 · Mathematics · Trigonometric Equations

The number of solutions in the interval [0, π] of the equation ^ 3...

The number of solutions in the interval [0,π]\left[0, \pi\right] of the equation sin⁡3xcos3x+sin⁡3xcos3x=0\sin^{3} xcos 3x + \sin 3x{cos}^{3} x = 0 is equal to

Options

  1. A77
  2. B66
  3. C55
  4. D44

Correct answer

C. 55

Step-by-step solution

The given equation can be written as
(3sinx−sin⁡3x4)cos⁡3x+sin⁡3x(3cosx+cos⁡3x4)\left(\dfrac{3sin x - \sin 3x}{4}\right)\cos 3x + \sin 3x\left(\dfrac{3cos x + \cos 3x}{4}\right)
sinxcos3x+cosxsin3x=0sin xcos3x + cos xsin 3x = 0
So, sin⁡(x+3x)=0⇒sin⁡4x=0\sin \left(x + 3x\right) = 0 ⇒ \sin 4x = 0
⇒x=nπ4,n∈Z.⇒ x = \dfrac{n\pi}{4}, n \in Z .
⇒x=0,π4,π2,3π4,π⇒ x = 0, \dfrac{\pi}{4}, \dfrac{\pi}{2}, \dfrac{3\pi}{4}, \pi
⇒5⇒ 5 solutions
Practice Trigonometric Equations on Quantrex Academy →

More from Trigonometric Equations

Match each entry in List-I to the correct entry in List-II and choose the correct option.… JEE Advanced 2026Passage: Consider the curve C_1 given by y = e^ -x for x ∈ [0, 10π] , and the curve C_2… JEE Advanced 2026Let S = \ θ ∈ (-2π, 2π) : θ + 1 = 3 θ\ . Then ∑_ θ ∈ S θ is equal to: JEE Main 2026If S = \ θ ∈ [-π, π] : θ (5θ)/(2) = 7θ (7θ)/(2)\ , then n(S) is equal to _______. JEE Main 2026Let S = \ x ∈ [-π, π] : x ( x + x) = a, a ∈ ℤ\ . Then n(S) is equal to : JEE Main 2026The number of elements in the set \ x ∈[0,180^ ∘ ]: (x+100^ ∘ )= (x+50^ ∘ ) x (x-50^ ∘ )\… JEE Main 2026Number of solutions of 3 2 θ+8 θ+3 3 =0, θ ∈[-3 π, 2 π] is: JEE Main 2026The number of solutions of the equation 2 θ (θ)/(2)+ (5 θ)/(2)=2 ^3 (5 θ)/(2) in… JEE Main 2025If for θ ∈[-(π)/(3), 0] , the points (x, y)=(3 (θ+(π)/(3)), 2 (θ+(π)/(6))) lie on x y+α… JEE Main 2025If 10 ^4 θ+15 ^4 θ=6 , then the value of 27 cosec^6 θ+8 ^6 θ 16 ^8 θ is: JEE Main 2025The number of solutions of equation (4- 3 ) x -2 3 ^2 x=- 4 1+ 3 , x ∈[-2 π, (5 π)/(2)] is JEE Main 2025The number of solutions of the equation 2 x+3 x=π, x ∈[-2 π, 2 π]-\ ± (π)/(2), ± (3… JEE Main 2025If θ ∈[-(7 π)/(6), (4 π)/(3)] , then the number of solutions of 3 cosec^2 θ-2( 3 -1)… JEE Main 2025If θ ∈[-2 π, 2 π] , then the number of solutions of 2 2 ^2 θ+(2- 6 ) θ- 3 =0 , is equal… JEE Main 2025The sum of all values of θ ∈[0,2 π] satisfying 2 ^2 θ= 2 θ and 2 ^2 θ=3 θ is JEE Main 2025Let f: ℝ arrow ℝ be a function defined by f(x)=\ array cc x^2 ((π)/(x^2)), & if x ≠ 0 0… JEE Advanced 2024 Full Trigonometric Equations list Trigonometric Equations JEE Maths PYQsJEE Mathematics PYQs All NTA Abhyas JEE Main PYQs