Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 20252 AprilEvening Shift
Exam
JEE Main
Year
2025
Date
2 April
Shift
Evening Shift
Subject
Mathematics
Chapter
Trigonometric Equations

JEE Main 2025 · 2 April · Evening Shift · Mathematics · Trigonometric Equations

If θ ∈[-(7 π)/(6), (4 π)/(3)] , then the number of solutions of 3...

If θ∈[−7π6,4π3]\theta \in\left[-\frac{7 \pi}{6}, \frac{4 \pi}{3}\right], then the number of solutions of 3cosec⁡2θ−2(3−1)cosec⁡θ−4=0\sqrt{3} \operatorname{cosec}^2 \theta-2(\sqrt{3}-1) \operatorname{cosec} \theta-4=0, is equal to

Options

  1. A66
  2. B88
  3. C1010
  4. D77

Correct answer

A. 66

Step-by-step solution

cosec⁡θ=2(3−1)±4(3+1−23)+16323=2(3−1)±16+8323=2(3−1)±(2+23)23\begin{aligned} & \operatorname{cosec} \theta=\frac{2(\sqrt{3}-1) \pm \sqrt{4(3+1-2 \sqrt{3})+16 \sqrt{3}}}{2 \sqrt{3}} \\ & =\frac{2(\sqrt{3-1}) \pm \sqrt{16+8 \sqrt{3}}}{2 \sqrt{3}} \\ & =\frac{2(\sqrt{3}-1) \pm(2+2 \sqrt{3})}{2 \sqrt{3}}\end{aligned}
cosec⁡θ=2\operatorname{cosec} \theta=2 or −23\frac{-2}{\sqrt{3}}
∴sin⁡θ=12\therefore \sin \theta=\frac{1}{2} or −32\frac{-\sqrt{3}}{2}
∴sin⁡θ=12\therefore \sin \theta=\frac{1}{2} has 3 solutions \& also sin⁡θ=−32\sin \theta=\frac{-\sqrt{3}}{2}
has 3 solutions in [−7π6,4π3]\left[\frac{-7 \pi}{6}, \frac{4 \pi}{3}\right]
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 ∈[-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 2024Let (π)/(2) < x < π be such that x= -5 11 . Then ( (11 x)/(2))( 6 x- 6 x)+( (11 x)/(2))(… JEE Advanced 2024 Full Trigonometric Equations list Trigonometric Equations JEE Maths PYQsJEE Mathematics PYQs All JEE Main PYQs