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Mathematics · Inverse Trigonometric Functions

JEE Main 2026 — 6 April, Morning Shift — Question 33

Let 0<α<1,β=13α0<\alpha<1, \beta=\frac{1}{3 \alpha} and tan⁡−1(1−α)+tan⁡−1(1−β)=π4\tan ^{-1}(1-\alpha)+\tan ^{-1}(1-\beta) =\frac{\pi}{4}. Then 6(α+β)6(\alpha+\beta) is equal to :

  1. Option A:

    66

  2. Option B:

    77

    Correct
  3. Option C:

    88

  4. Option D:

    99

Answer: B

Step-by-step solution

β=13α,tan⁡−1(1−α)+tan⁡−1(1−β)=π4\beta=\frac{1}{3 \alpha}, \tan ^{-1}(1-\alpha)+\tan ^{-1}(1-\beta)=\frac{\pi}{4} ⇒tan⁡(tan⁡−1(1−α)+tan⁡−1(1−β))=1\Rightarrow \tan \left(\tan ^{-1}(1-\alpha)+\tan ^{-1}(1-\beta)\right)=1 ⇒1−α+1−β1−(1−α)(1−β)=1\Rightarrow \frac{1-\alpha+1-\beta}{1-(1-\alpha)(1-\beta)}=1 ⇒2−α−β=1−(1−α−β+αβ)\Rightarrow 2-\alpha-\beta=1-(1-\alpha-\beta+\alpha \beta) ⇒2−α−β=α+β−αβ\Rightarrow 2-\alpha-\beta=\alpha+\beta-\alpha \beta ⇒2(α+β)=2+αβ\Rightarrow 2(\alpha+\beta)=2+\alpha \beta ⇒2(α+β)=2+13=73\Rightarrow 2(\alpha+\beta)=2+\frac{1}{3}=\frac{7}{3} α+β=76\alpha+\beta=\frac{7}{6} 6(α+β)=76(\alpha+\beta)=7

Answer key and solution verified before publishing.

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Exam
JEE Main 2026
Paper
6 April, Morning Shift
Subject
Mathematics
Chapter
Inverse Trigonometric Functions
Topic
Properties related to Inverse Trigonometric Functions
Let 0<α<1, β=1/3 α and tan -1 (1-α)+tan -1 (1-β) =π/4 . Then 6(α+β)… | JEE Main 2026 PYQ with Solution · DhiX AI