JEE Main 2021MathematicsTrigonometric Ratios & IdentitiesMediumMCQ

JEE Main 2021 — Trigonometric Ratios & Identities Question with Solution

JEE Main 2021 (27 Jul Shift 1)

Question

If sinθ+cosθ=12, then 16sin2θ+cos4θ+sin6θ is equal to:

Choose an option

Show full solutionCorrect option: C
Correct answer
C-23

Step-by-step explanation

sinθ+cosθ=12

sin2θ+cos2θ+2sinθcosθ=14⇒sin2θ=-34

Now:

cos4θ=1-2sin22θ

=1-2-342

=1-2×916=-18

And sin6θ=3sin2θ-4sin32θ

=3-4sin22θ·sin2θ

=3-4916·-34

=34×-34=-916

So, 16sin2θ+cos4θ+sin6θ

=16-34-18-916=-23

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About this question

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