JEE Main 2022 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 25 July 2022, Shift 2, Maths Q30

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

Let

x=\sin\left(2\tan^{-1}\alpha\right)

and

y=\sin\left(\frac{1}{2}\tan^{-1}\frac{4}{3}\right)

. If

S=\{\alpha\in\mathbb{R}:y^2=1-x\}

, then

\sum_{\alpha\in S}16\alpha^3

is equal to ___________.

Official answer

130

NTA final key.

Chapter: Inverse Trigonometric Functions
Topic: Inverse Trig Identities
Idea tested: 2tan-1(x) to sin-1 and cos-1 Conversions

Same topic in other shifts

All Inverse Trig Identities questions

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