If sin (tan -1 (x√(2)) ) = cot (sin -1 √(1-x 2) ) , xin (0,1) , then the value of x is :

Mathematics · Inverse Trigonometric Functions

JEE Main 2026 — 6 April, Evening Shift — Question 32

If $\sin \left(\tan^{-1}(x\sqrt{2})\right) = \cot \left(\sin^{-1}\sqrt{1-x^2}\right)$ , $x\in (0,1)$ , then the value of x is :

Option A:
$\frac{1}{2}$
Correct
Option B:
$\frac{1}{3}$
Option C:
$\frac{2}{3}$
Option D:
$\frac{5}{8}$

Answer: A

Step-by-step solution

$\frac{x \sqrt{2}}{\sqrt{2 x^{2}+1}}=\frac{1}{\sqrt{1-x^{2}}}$ $2\left(1-x^{2}\right)=\left(2 x^{2}+1\right)$ $2-2 \mathrm{x}^{2}=2 \mathrm{x}^{2}+1$ $\mathrm{x}^{2}=\frac{1}{4}$ $\mathrm{x}=\frac{1}{2}$

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Exam: JEE Main 2026
Paper: 6 April, Evening Shift
Subject: Mathematics
Chapter: Inverse Trigonometric Functions
Topic: Properties related to Inverse Trigonometric Functions