JEE Main 2019MathematicsTrigonometric Ratios & IdentitiesMediumMCQ

JEE Main 2019 — Trigonometric Ratios & Identities Question with Solution

JEE Main 2019 (12 Apr Shift 1)

Question

The equation y=sinxsin⁡x+2-sin2⁡(x+1) represents a straight line lying in:

Choose an option

Show full solutionCorrect option: D
Correct answer
Dthird and fourth quadrants only

Step-by-step explanation

y=sin⁡(x+2)sin⁡x-sin2⁡x+1
=122sin⁡x+2sin⁡x-2sin2⁡x+1

 ∵ 2sin⁡Asin⁡B =cos⁡A-B-cos⁡A+B & cos⁡2A=1-2sin2⁡A
=12cos⁡x+2-x-cos⁡2x+2-1-cos⁡2x+1
=12cos⁡2-cos⁡2x+2-1+cos⁡2x+2
=121-cos⁡2=-122sin2⁡1
=-sin2⁡1 ( constant and negative )

Hence, the straight line lies in the third and fourth quadrants only.

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About this question

This is a previous-year question from JEE Main 2019, covering the Trigonometric Ratios & Identities 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.