JEE Main 2021MathematicsSequences and SeriesEasyMCQ

JEE Main 2021 — Sequences and Series Question with Solution

JEE Main 2021 (27 Jul Shift 2)

Question

If tanπ9,x,tan7π18 are in arithmetic progression and tanπ9,y,tan5π18 are also in arithmetic progression, then x-2y is equal to :

Choose an option

Show full solutionCorrect option: C
Correct answer
C0

Step-by-step explanation

x=12tanπ9+tan7π18

and 2y=tanπ9+tan5π18

so, x-2y=12tanπ9+tan7π18-tanπ9+tan5π18

⇒x-2y=cotπ9-tanπ92-tan5π18

⇒x-2y=cot2π9-12cotπ9-tan5π18

⇒x-2y=cot2π9-tan5π18

=0

∵tan5π18=cotπ2-5π18=cot2π9∵tan7π18=cotπ2-7π18=cotπ9

∵cot2θ-12cotθ=cot2θ

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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.