JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 30 July 2022, Shift 2, Maths Q90

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

Let

S = \left\{\theta \in [0, 2\pi] - \left\{\frac{\pi}{2}, \frac{3\pi}{2}\right\} : \sin^{-1}(\sin\theta) + \cos^{-1}(\cos\theta) + \tan^{-1}(\tan\theta) = \frac{4\pi}{5}\right\}

. Then

\frac{30}{\pi}\sum_{\theta \in S} \theta

is equal to ________.

Official answer

NTA final key.

Chapter: Inverse Trigonometric Functions
Topic: Inverse Trig Identities
Idea tested: Extreme Value Principle in Equations

Same topic in other shifts

All Inverse Trig Identities questions

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