JEE Main 2019MathematicsInverse Trigonometric FunctionsMediumMCQ

JEE Main 2019 — Inverse Trigonometric Functions Question with Solution

JEE Main 2019 (12 Jan Shift 1)

Question

Considering only the principal values of inverse functions, the set A=x≥0 : tan-12x+tan-13x=π4

Choose an option

Show full solutionCorrect option: D
Correct answer
DIs a singleton

Step-by-step explanation

Given tan-12x+tan-13x=π4

⇒tan-12x+3x1-2x×3x=π4

Applying tangent on both sides,

⇒5x1-6x2=1 ∵tanπ4=1

⇒5x=1-6x2

⇒6x2+5x-1=0

⇒6x2+6x-x-1=0

⇒6x-1x+1=0

⇒x=-1, 16

But, since x≥0.

Hence, x=16

∴ A has only one element and thus, it is a singleton.

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About this question

This is a previous-year question from JEE Main 2019, 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.