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JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 27 August 2021, Shift 2, Maths Q67

Question 67 of 90 in this shift, Maths question 7 of 30, Section A.

If

y(x) = \cot^{-1}\left(\frac{\sqrt{1+\sin x} + \sqrt{1-\sin x}}{\sqrt{1+\sin x} - \sqrt{1-\sin x}}\right), x \in \left(\frac{\pi}{2}, \pi\right)

, then

\frac{dy}{dx}

at

x = \frac{5\pi}{6}

is :

(1) $\frac{1}{2}$
(2) $-\frac{1}{2}$ Official answer
(3) $0$
(4) $-1$

Official answer

Option 2

NTA final key.

Chapter: Continuity and Differentiability
Topic: Inverse Trig Identities
Idea tested: Periodic Reduction of tan-1(tan x) and cot-1(cot x)

Same idea in other shifts

Asked 2× in all

9 Jan 2020, Shift 1 · Q61If $f'(x)=\tan^{-1}(\sec x+\tan x)$ , $-\frac{\pi}{2}<x<\frac{\pi}{2}$ , and $f(0)=0$ , then $f(1)$ is equal to :HardSingle 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.