JEE Main 2021MathematicsSequences and SeriesMediumMCQ

JEE Main 2021 — Sequences and Series Question with Solution

JEE Main 2021 (24 Feb Shift 1)

Question

If ecos2x+cos4x+cos6x+....∞loge2 satisfies the equation t2-9t+8=0, then the value of 2sinxsinx+3cosx, where 0<x<π2, is equal to

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Show full solutionCorrect option: B
Correct answer
B12

Step-by-step explanation

ecos2x+cos4x+……∞ln 2=2cos2x+cos4x+……∞

==2cos2x1-cos2x=2cot2x

t2-9t+8=0⇒t=1,8

⇒2cot2x=1, 8⇒cot2x=0,3

0<x<π2⇒cot x=3

⇒2 sin xsin x+3 cos x=21+3 cot x=24=12

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About this question

This is a previous-year question from JEE Main 2021, covering the Sequences and Series 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.