JEE Main 2022MathematicsInverse Trigonometric FunctionsHardMCQ

JEE Main 2022 — Inverse Trigonometric Functions Question with Solution

JEE Main 2022 (26 Jul Shift 2)

Question

If 0<x<12 and sin-1xα=cos-1xβ, then a value of sin2παα+β is

Choose an option

Show full solutionCorrect option: B
Correct answer
B4x1-x21-2x2

Step-by-step explanation

Let sin-1xα=cos-1xβ=k

i.e. sin-1x=kα and cos-1x=kβ

⇒sin-1x+cos-1x=kα+β

i.e. kα+β=π2

⇒k=π2α+β

Now 2παα+β=4kα=4sin-1x

So sin2παα+β=sin4sin-1x

=2sin2sin-1xcos2sin-1x

=2sinsin-12x1-x2cossin-12x1-x2

=2sinsin-12x1-x2coscos-11-2x2

=4x1-x21-2x2

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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.