JEE Main 2019MathematicsTrigonometric EquationsMediumMCQ

JEE Main 2019 — Trigonometric Equations Question with Solution

JEE Main 2019 (12 Apr Shift 2)

Question

Let S be the set of all α ∈ R such that the equation, cos2x+αsinx=2α-7 has a solution. Then S is equal to:

Choose an option

Show full solutionCorrect option: B
Correct answer
B2, 6

Step-by-step explanation

The given equation can be written as:
1-2sin2⁡x+ α sinx=2α-7
⇒2sin2⁡x-αsin⁡x+2α-8=0
⇒sinx=α-4 2,  2 sinx ≠2
For at least one solution
-1≤α-42 ≤1
⇒α∈[2,6]

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About this question

This is a previous-year question from JEE Main 2019, covering the Trigonometric Equations chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.