JEE Main 2023MathematicsTrigonometric EquationsMediumMCQ

JEE Main 2023 — Trigonometric Equations Question with Solution

JEE Main 2023 (10 Apr Shift 2)

Question

Let S=x∈-π2,π2:91-tan2x+9tan2x=10 and β=∑x∈Stan2x3, then 16(β-14)2 is equal to

Choose an option

Show full solutionCorrect option: D
Correct answer
D32

Step-by-step explanation

Given,

91-tan2x+9tan2x=10

Now let 9tan2x=t, then above equation will be,

9t+t=10

⇒t2-10t+9=0

⇒t=9 or t=1

So, when 9tan2x=9⇒tan2x=1

⇒tanx=±1⇒x=±π4, as given x∈-π2,π2

Now when 9tan2x=1

⇒tan2x=0⇒x=0

Hence, β=∑x∈Sx3=tan203+tan2π12+tan2-π12

=0+22-32

=14-83

So, the value of 16β-142=64×36=32

Hence this is the correct option.

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About this question

This is a previous-year question from JEE Main 2023, 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.