JEE Main 2022MathematicsTrigonometric EquationsMediumMCQ

JEE Main 2022 — Trigonometric Equations Question with Solution

JEE Main 2022 (26 Jul Shift 1)

Question

Let S=θ∈0,2π:82sin2θ+82cos2θ=16. Then nS+∑θ∈Ssecπ4+2θcosecπ4+2θ is equal to:

Choose an option

Show full solutionCorrect option: C
Correct answer
C-4

Step-by-step explanation

Given, 82sin2θ+82cos2θ=16

⇒82sin2θ+82-2sin2θ=16

Now let 82sin2θ=y 

⇒y+64y=16

⇒  y=8

⇒82sin2θ=8

⇒sin2θ=12

⇒θ∈π4,3π4,5π4,7π4

Now nS+∑θ∈Ssecπ4+2θcosecπ4+2θ

 =nS+∑θ∈S1cosπ4+2θsinπ4+2θ

=4+∑θ∈S22cosπ4+2θsinπ4+2θ

=4+∑θ∈S2cosecπ2+4θ

=4+2cosecπ2+π+2cosecπ2+3π+2cosecπ2+5π+2cosecπ2+7π

=4+2-cosecπ2-cosecπ2-cosecπ2-cosecπ2

=4+-2×4=-4

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 2022, 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.