JEE Main 2022MathematicsInverse Trigonometric FunctionsMediumNumerical

JEE Main 2022 — Inverse Trigonometric Functions Question with Solution

JEE Main 2022 (25 Jul Shift 2)

Question

Let x=sin2tan-1α and y=sin12tan-143. If S=α∈ℝ:y2=1-x, then ∑α∈S16α3 is equal to _______.

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Show full solutionCorrect answer: 130
Correct answer
130

Step-by-step explanation

Given x=sin2tan-1α=sintan-12α1-α2=sinsin-12α1+α2=2α1+α2    ⋯i

and y=sin12tan-143=sintan-112=sinsin-115=15   ...ii

Now, y2=1-x

⇒15=1-2α1+α2 (from i & ii)

⇒1+α2=5+5α2-10α

⇒ 2α2-5α+2=0

∴ α=2,12

∴ ∑α∈S16α3=16×23+16×123=16658

=130

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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.