JEE Main 2019MathematicsTrigonometric EquationsMediumMCQ

JEE Main 2019 — Trigonometric Equations Question with Solution

JEE Main 2019 (10 Apr Shift 1)

Question

All the pairs (x, y), that satisfy the inequality 2sin2x-2sinx+5·14sin2y≤1 also satisfy the equation:

Choose an option

Show full solutionCorrect option: C
Correct answer
Csinx=siny

Step-by-step explanation

Given inequality is
2sin2⁡x-2sin⁡x+5 ≤4sin2⁡y
⇒sin2⁡x-2sin⁡x+1+4≤2sin2⁡y
⇒sin⁡x-12+4≤2sin2⁡y
∵2sin2⁡y∈0, 2  &  sin⁡x-12+4∈2, 22
∵  Only equality holds
⇒sin⁡x-12+4=2sin2⁡y=2
⇒sin⁡x-12+4=4sin4⁡y=4 
⇒sin2⁡y=1   ⇒  sin⁡y=1   &  sin⁡x-12=0 ⇒sin⁡x=1
∴sin⁡y=sin⁡x

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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.