JEE Main 2020 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 8 January 2020, Shift 1, Maths Q69

Question 69 of 75 in this shift, Maths question 19 of 25, Section A.

Let

f(x)=\left(\sin(\tan^{-1}x)+\sin(\cot^{-1}x)\right)^2-1

|x|>1

. If

\dfrac{dy}{dx}=\dfrac{1}{2}\dfrac{d}{dx}\left(\sin^{-1}(f(x))\right)

and

y(\sqrt{3})=\frac{\pi}{6}

, then

y(-\sqrt{3})

is equal to :

(1) $-\frac{\pi}{6}$
(2) $\frac{2\pi}{3}$
(3) $\frac{5\pi}{6}$ Official answer
(4) $\frac{\pi}{3}$

Official answer

Option 3

NTA final key (Jan 2020).

Chapter: Inverse Trigonometric Functions
Topic: Inverse Trig Identities
Idea tested: sin^-1(2x/(1+x^2)) Piecewise Conversion

Same topic in other shifts

All Inverse Trig Identities questions

4 Apr 2026, Shift 1 · Q16If $y=\tan^{-1}\left(\frac{3\cos x-4\sin x}{4\cos x+3\sin x}\right)+2\tan^{-1}\left(\frac{x}{1+\sqrt{1-x^2}}\right)$ , then $\frac{dy}{dx}$ …MediumSingle correct
4 Apr 2026, Shift 2 · Q20The integral $\int_0^1\cot^{-1}\left(1+x+x^2\right)dx$ is equal to:HardSingle correct
5 Apr 2026, Shift 1 · Q24If $\frac{\pi}{4} + \sum_{p=1}^{11} \tan^{-1}\left(\frac{2^{p-1}}{1 + 2^{2p-1}}\right) = \alpha$ , then $\tan\alpha$ is equal to ________.MediumNumerical value
6 Apr 2026, Shift 1 · Q13Let $0<\alpha<1$ , $\beta=\frac{1}{3\alpha}$ and $\tan^{-1}(1-\alpha)+\tan^{-1}(1-\beta)=\frac{\pi}{4}$ . Then $6(\alpha+\beta)$ is equal to:MediumSingle correct
6 Apr 2026, Shift 2 · Q13If $\sin\left(\tan^{-1}\left(x\sqrt{2}\right)\right)=\cot\left(\sin^{-1}\sqrt{1-x^2}\right)$ , $x\in(0,1)$ , then the value of $x$ is :MediumSingle correct
8 Apr 2026, Shift 2 · Q12Let $\alpha = 3\sin^{-1}\left(\frac{6}{11}\right)$ and $\beta = 3\cos^{-1}\left(\frac{4}{9}\right)$ , where inverse trigonometric functions…HardTwo statements

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 42 of the 174 JEE Main shifts held from 2017 to 2026.