JEE Main 2021MathematicsTrigonometric EquationsMediumMCQ

JEE Main 2021 — Trigonometric Equations Question with Solution

JEE Main 2021 (25 Feb Shift 1)

Question

All possible values of θ∈0,2π for which sin2θ+tan2θ>0 lie in :

Choose an option

Show full solutionCorrect option: C
Correct answer
C0,π4∪π2,3π4∪π,5π4∪3π2,7π4

Step-by-step explanation

sin2θ+tan2θ>0

⇒sin2θ+sin2θcos2θ>0

⇒sin2θcos2θ+1cos2θ>0⇒tan2θ2cos2θ>0

Note: cos2θ≠0

⇒1-2sin2θ≠0⇒sinθ≠±12

Now, tan2θ1+cos2θ>0

⇒tan2θ>0 (as cos2θ+1>0)

⇒2θ∈0,π2∪π,3π2∪2π,5π2∪3π,7π2

⇒θ∈0,π4∪π2,3π4∪π,5π4∪3π2,7π4

As sinθ≠±12; which has been already considered

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About this question

This is a previous-year question from JEE Main 2021, 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.