JEE Main 2019MathematicsTrigonometric EquationsMediumMCQ

JEE Main 2019 — Trigonometric Equations Question with Solution

JEE Main 2019 (09 Apr Shift 1)

Question

Let  S=θ∈-2π,2π:2cos2θ+3sinθ=0. Then the sum of the elements of S is:

Choose an option

Show full solutionCorrect option: D
Correct answer
D2π

Step-by-step explanation

The given equation 2cos2θ+3sinθ=0 can be written as

21-sin2θ+3sinθ=0

⇒2sin2θ-3sinθ-2=0

⇒2sinθ+1sinθ-2=0

⇒sinθ=2, -12, sinθ≠2

⇒sinθ=-12

Hence, solutions in -2π, 2π are
-π+π6, -π6, π+π6, 2π-π6

Sum of the elements is =2π.

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Trigonometric Equations chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

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.