Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 201323 AprilOnline
Exam
JEE Main
Year
2013
Date
23 April
Mode
Online
Subject
Mathematics
Chapter
Trigonometric Equations

JEE Main 2013 · 23 April · Online · Mathematics · Trigonometric Equations

The number of solutions of the equation 2 x-2 x+4 x=4 in the...

The number of solutions of the equation sin⁡2x−2cos⁡x+4sin⁡x=4\sin 2 x-2 \cos x+4 \sin x=4 in the interval [0,5π][0,5 \pi] is :

Options

  1. A3
  2. B5
  3. C4
  4. D6

Correct answer

A. 3

Step-by-step solution

sin⁡2x−2cos⁡x+4sin⁡x=4⇒2sin⁡x⋅\cosx−2cos⁡x+4sin⁡x−4=0⇒(sin⁡x−1)(cos⁡x−2)=0\begin{aligned}& \sin 2 x-2 \cos x+4 \sin x=4 \\ & \Rightarrow 2 \sin x \cdot \cosx-2 \cos x+4 \sin x-4=0 \\ & \Rightarrow(\sin x-1)(\cos x-2)=0 \end{aligned}∵cos⁡x−2≠0,∴sin⁡x=1∴x=π2,5π2,9π2\begin{aligned}& \because \cos x-2 ≠ 0, \therefore \sin x=1 \\ & \therefore \quad x=\frac{\pi}{2}, \frac{5 \pi}{2}, \frac{9 \pi}{2} \end{aligned}
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 JEE Main PYQs