JEE Main 2022MathematicsInverse Trigonometric FunctionsEasyMCQ

JEE Main 2022 — Inverse Trigonometric Functions Question with Solution

JEE Main 2022 (28 Jul Shift 1)

Question

Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the equation cos-1x-2sin-1x=cos-12x is equal to

Choose an option

Show full solutionCorrect option: A
Correct answer
A0

Step-by-step explanation

Given,

cos-1x-2sin-1x=cos-12x

⇒cos-1x-2π2-cos-1x=cos-12x

⇒cos-1x-π+2cos-1x=cos-12x

⇒3cos-1x=π+cos-12x     ...1

Taking cos both side we get,

⇒cos3cos-1x=cosπ+cos-12x

⇒coscos-14x3-3x=-coscos-12x

⇒4x3-3x=-2x

⇒4x3=x

⇒x=0,±12

All will satisfy the original equation,

So, sum of all the solution will be 0+12-12=0

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Inverse Trigonometric Functions chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

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.