JEE Main 2024MathematicsInverse Trigonometric FunctionsEasyMCQ

JEE Main 2024 — Inverse Trigonometric Functions Question with Solution

JEE Main 2024 (27 Jan Shift 2)

Question

Considering only the principal values of inverse trigonometric functions, the number of positive real values of x satisfying tan-1(x)+tan-1(2x)=π4 is :

Choose an option

Show full solutionCorrect option: B
Correct answer
B1

Step-by-step explanation

Let, 

fx=tan-1x+tan-12x

Now, differentiating the above function we get,

⇒f'x=11+x2+21+4x2

⇒f'x>0; ∀x∈R

⇒limx→∞fx=π and limx→-∞fx=-π

Hence, fx is monotonically increasing for x∈R and the range of fx is -π,π.

Hence, fx=π4 has exactly one solution for x>0.

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About this question

This is a previous-year question from JEE Main 2024, 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.