Start free

Mathematics · Inverse Trigonometric Functions

JEE Main 2024 — 27 January, Shift 2 — Question 1

Considering only the principal values of inverse trigonometric functions, the number of positive real values of xx satisfying tan⁡−1(x)+tan⁡−1(2x)=π4\tan ^{-1}(x)+\tan ^{-1}(2 x)=\frac{\pi}{4} is :

  1. Option A:

    More than 2

  2. Option B:

    1

    Correct
  3. Option C:

    2

  4. Option D:

    0

Answer: B

Step-by-step solution

tan⁡−1x+tan⁡−12x=π4;x>0\tan ^{-1} \mathrm{x}+\tan ^{-1} 2 \mathrm{x}=\frac{\pi}{4} ; \mathrm{x}>0

⇒tan⁡−12x=π4−tan⁡−1x\Rightarrow \tan ^{-1} 2 x=\frac{\pi}{4}-\tan ^{-1} x

Taking tan both sides ⇒2x=1−x1+x\Rightarrow 2 \mathrm{x}=\frac{1-\mathrm{x}}{1+\mathrm{x}}

⇒2x2+3x−1=0\Rightarrow 2 x^{2}+3 \mathrm{x}-1=0

x=−3±9+88=−3±178x=\frac{-3 \pm \sqrt{9+8}}{8}=\frac{-3 \pm \sqrt{17}}{8}

Only possible x=−3+178\mathrm{x}=\frac{-3+\sqrt{17}}{8}

Answer key and solution verified before publishing.

Practise Inverse Trigonometric Functions

Start with this question, then two more from the same chapter — with a tutor that explains every step. Free.

Solve a similar one free
Exam
JEE Main 2024
Paper
27 January, Shift 2
Subject
Mathematics
Chapter
Inverse Trigonometric Functions
Topic
Equations, Inequations and Identitites involving ITFs
Considering only the principal values of inverse trigonometric… | JEE Main 2024 PYQ with Solution · DhiX AI