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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctEasyCalculation

JEE Main 26 June 2022, Shift 2, Maths Q19

Question 19 of 90 in this shift, Maths question 19 of 30, Section A.

If the inverse trigonometric functions take principal values, then cos⁡−1(310cos⁡(tan⁡−1(43))+25sin⁡(tan⁡−1(43)))\cos^{-1}\left(\frac{3}{10}\cos\left(\tan^{-1}\left(\frac{4}{3}\right)\right) + \frac{2}{5}\sin\left(\tan^{-1}\left(\frac{4}{3}\right)\right)\right) is equal to :
  1. (1)00
  2. (2)π4\frac{\pi}{4}
  3. (3)π3\frac{\pi}{3}Official answer
  4. (4)π6\frac{\pi}{6}

Official answer

Option 3

NTA final key.

Chapter
Inverse Trigonometric Functions
Topic
Inverse Trig Identities
Idea tested
Evaluating Trig of Inverse Trig

Same idea in other shifts

Asked 3× in all
  1. 6 Apr 2026, Shift 2 · Q13If sin⁡(tan⁡−1(x2))=cot⁡(sin⁡−11−x2)\sin\left(\tan^{-1}\left(x\sqrt{2}\right)\right)=\cot\left(\sin^{-1}\sqrt{1-x^2}\right), x∈(0,1)x\in(0,1), then the value of xx is :MediumSingle correct
  2. 27 Jul 2022, Shift 1 · Q21For k∈Rk \in \mathbb{R}, let the solutions of the equation…HardNumerical value

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.