Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 201912 AprilEvening Shift
Exam
JEE Main
Year
2019
Date
12 April
Shift
Evening Shift
Subject
Mathematics
Chapter
Trigonometric Equations

JEE Main 2019 · 12 April · Evening Shift · Mathematics · Trigonometric Equations

Let S be the set of all α ∈ R such that the equation, 2x + α sinx =...

Let SS be the set of all α∈R\alpha \in R such that the equation, cos⁡2x+αsinx=2α−7\cos 2x + \alpha sinx = 2\alpha - 7 has a solution. Then SS is equal to:

Options

  1. A[3,7]\left[3, 7\right]
  2. B[2,6]\left[2, 6\right]
  3. C[1,4]\left[1, 4\right]
  4. DR

Correct answer

B. [2,6]\left[2, 6\right]

Step-by-step solution

The given equation can be written as:
1−2sin⁡2x+αsinx=2α−71 - 2\sin^{2} x + \alpha sinx = 2\alpha - 7
⇒2sin⁡2x−αsinx+2α−8=0⇒ 2\sin^{2} x - \alpha sin x + 2\alpha - 8 = 0
⇒sin⁡x=α−42,2⇒ \sin x = \dfrac{\alpha - 4}{2}, 2\left(\sin x \ne 2\right)<br/>Foratleastonesolution<br/><br/>For at least one solution <br/>- 1 \le \dfrac{\alpha - 4}{2} \le 1<br/><br/>⇒ \alpha \in [ 2,6 ]
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