JEE Main 2023 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 13 April 2023, Shift 1, Maths Q30

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

S=\left\{x\in\mathbb{R}:\sin^{-1}\left(\frac{x+1}{\sqrt{x^2+2x+2}}\right)-\sin^{-1}\left(\frac{x}{\sqrt{x^2+1}}\right)=\frac{\pi}{4}\right\}

, then

\sum_{x\in s}\left(\sin\left((x^2+x+5)\frac{\pi}{2}\right)-\cos\left((x^2+x+5)\pi\right)\right)

is equal to ________.

Official answer

NTA final key.

Chapter: Inverse Trigonometric Functions
Topic: Inverse Trig Identities
Idea tested: Sine Inverse Sum and Difference

Same idea in other shifts

Asked 3× in all

16 Mar 2021, Shift 2 · Q78Given that the inverse trigonometric functions take principal values only. Then, the number of real values of $x$ which satisfy…MediumSingle correct
3 Sep 2020, Shift 1 · Q69 $2\pi-\left(\sin^{-1}\frac{4}{5}+\sin^{-1}\frac{5}{13}+\sin^{-1}\frac{16}{65}\right)$ 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.