JEE Main 2022MathematicsInverse Trigonometric FunctionsHardMCQ

JEE Main 2022 — Inverse Trigonometric Functions Question with Solution

JEE Main 2022 (28 Jun Shift 2)

Question

The value of limn→∞6tan∑r=1ntan-11r2+3r+3 is equal to

Choose an option

Show full solutionCorrect option: C
Correct answer
C3

Step-by-step explanation

Let S=∑r=1ntan-11r2+3r+3

So, Tr=tan-11r2+3r+2+1

=tan-1(r+2)-(r+1)1+(r+1)(r+2)

=tan-1r+2-tan-1r+1

T1=tan-13-tan-12

T2=tan-14-tan-13..
Tn=tan-1n+2-tan-1n+1

⇒∑r=1ntan-11r2+3r+3=tan-1n+2-tan-12

i.e. 6tanlimn→∞∑r=1ntan-11r2+3r+3=6tanlimn→∞∑r=1ntan-1n+2-tan-12

=6tanπ2-tan-12

=6tantan-112=3

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About this question

This is a previous-year question from JEE Main 2022, covering the Inverse Trigonometric Functions 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.