JEE Main 2014MathematicsTrigonometric Ratios & IdentitiesHardMCQ

JEE Main 2014 — Trigonometric Ratios & Identities Question with Solution

JEE Main 2014 (06 Apr)

Question

Let fkx=1ksink x+cosk x where x∈R and k≥1. Then f4x-f6x equals 

Choose an option

Show full solutionCorrect option: B
Correct answer
B 1 1 2

Step-by-step explanation

f4x=14sin4x+cos4x

=14sin2x+cos2x2-2sin2x cos2x

=141-2sin2x cos2x

f6x=16sin6x+cos6x

=16sin2x+cos2x3-3sin2x cos2xsin2x+cos2x

=161-3sin2x cos2x1

f4x-f6x=14-16

=112

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About this question

This is a previous-year question from JEE Main 2014, 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.