JEE Main 2022 · MathsNumerical answerNumerical valueMediumCalculation

JEE Main 29 June 2022, Shift 1, Maths Q26

Question 26 of 90 in this shift, Maths question 26 of 30, Section B.

50\tan\left(3\tan^{-1}\left(\frac{1}{2}\right) + 2\cos^{-1}\left(\frac{1}{\sqrt{5}}\right)\right) + 4\sqrt{2}\tan\left(\frac{1}{2}\tan^{-1}(2\sqrt{2})\right)

is equal to ____________.

Official answer

NTA final key (2022 Session 1).

Chapter: Inverse Trigonometric Functions
Topic: Inverse Trig Identities
Idea tested: Trig of Sum of Inverse Trig Functions

Same idea in other shifts

Asked 4× in all

2 Apr 2025, Shift 2 · Q23If $y = \cos\left(\frac{\pi}{3} + \cos^{-1}\frac{x}{2}\right)$ , then $(x-y)^2 + 3y^2$ is equal to __________.MediumNumerical value
30 Jun 2022, Shift 1 · Q19Let $\alpha = \tan\left(\frac{5\pi}{16}\sin\left(2\cos^{-1}\left(\frac{1}{\sqrt{5}}\right)\right)\right)$ and…MediumSingle correct
25 Feb 2021, Shift 2 · Q79 $\mathrm{cosec}\left[2\cot^{-1}(5) + \cos^{-1}\left(\frac{4}{5}\right)\right]$ is equal to :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.