JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 26 July 2022, Shift 1, Maths Q18

Question 18 of 90 in this shift, Maths question 18 of 30, Section A.

Let

\mathrm{S} = \{\theta \in [0,\ 2\pi] : 8^{2\sin^2\theta} + 8^{2\cos^2\theta} = 16\}

. Then

\mathrm{n}(\mathrm{S}) + \sum_{\theta \in \mathrm{S}} \left(\sec\left(\frac{\pi}{4} + 2\theta\right) \mathrm{cosec}\left(\frac{\pi}{4} + 2\theta\right)\right)

is equal to :

(1) $0$
(2) $-2$
(3) $-4$ Official answer
(4) $12$

Official answer

Option 3

NTA final key.

Chapter: Trigonometric Functions
Topic: General Solutions
Idea tested: Quadratic Substitution in Trigonometry

Same idea in other shifts

Asked 12× in all

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11 Apr 2023, Shift 1 · Q16The number of elements in the set $S = \{\theta \in [0, 2\pi] : 3\cos^4\theta - 5\cos^2\theta - 2\sin^6\theta + 2 = 0\}$ isMediumSingle correct
29 Jun 2022, Shift 1 · Q24The number of elements in the set $S = \{\theta \in [-4\pi, 4\pi] : 3\cos^2 2\theta + 6\cos 2\theta - 10\cos^2\theta + 5 = 0\}$ is…MediumNumerical 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.