JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 26 July 2022, Shift 2, Maths Q16

Question 16 of 90 in this shift, Maths question 16 of 30, Section A.

0<x<\frac{1}{\sqrt{2}}

and

\frac{\sin^{-1}x}{\alpha}=\frac{\cos^{-1}x}{\beta}

, then a value of

\sin\left(\frac{2\pi\alpha}{\alpha+\beta}\right)

(1) $4\sqrt{1-x^2}\left(1-2x^2\right)$
(2) $4x\sqrt{1-x^2}\left(1-2x^2\right)$ Official answer
(3) $2x\sqrt{1-x^2}\left(1-4x^2\right)$
(4) $4\sqrt{1-x^2}\left(1-4x^2\right)$

Official answer

Option 2

NTA final key.

Chapter: Inverse Trigonometric Functions
Topic: Inverse Trig Identities
Idea tested: Complementary Identities

Same idea in other shifts

Asked 7× in all

4 Apr 2024, Shift 2 · Q20Given that the inverse trigonometric function assumes principal values only. Let $x$ , $y$ be any two real numbers in $[-1,1]$ such that…HardSingle correct
9 Apr 2024, Shift 2 · Q30Let the inverse trigonometric functions take principal values. The number of real solutions of the equation…MediumNumerical value
24 Jun 2022, Shift 1 · Q8The set of all values of k for which $(\tan^{-1}x)^3 + (\cot^{-1}x)^3 = k\pi^3,\ x \in \mathbf{R}$ , is the interval :HardSingle correct
30 Jun 2022, Shift 1 · Q10Let m and M respectively be the minimum and the maximum values of $f(x) = \sin^{-1}2x + \sin 2x + \cos^{-1}2x + \cos 2x$ ,…MediumSingle correct
27 Aug 2021, Shift 1 · Q76If $(\sin^{-1}x)^2-(\cos^{-1}x)^2=a$ ; $0<x<1$ , $a\neq 0$ , then the value of $2x^2-1$ is :MediumSingle correct
26 Feb 2021, Shift 1 · Q76If $\frac{\sin^{-1}x}{a}=\frac{\cos^{-1}x}{b}=\frac{\tan^{-1}y}{c}$ ; $0<x<1$ , then the value of $\cos\left(\frac{\pi c}{a+b}\right)$ is :MediumSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.