JEE Main 2022 · MathsMultiple choiceSingle correctEasyApplication

JEE Main 28 June 2022, Shift 2, Maths Q20

Question 20 of 90 in this shift, Maths question 20 of 30, Section A.

\cot\alpha=1

and

\sec\beta=-\frac{5}{3}

, where

\pi<\alpha<\frac{3\pi}{2}

and

\frac{\pi}{2}<\beta<\pi

, then the value of

\tan(\alpha+\beta)

and the quadrant in which

\alpha+\beta

lies, respectively are :

(1) $-\frac{1}{7}$ and $\mathrm{IV^{th}}$ quadrantOfficial answer
(2)7 and $\mathrm{I^{st}}$ quadrant
(3) $-7$ and $\mathrm{IV^{th}}$ quadrant
(4) $\frac{1}{7}$ and $\mathrm{I^{st}}$ quadrant

Official answer

Option 1

NTA final key.

Chapter: Trigonometric Functions
Topic: Trigonometric Identities
Idea tested: Compound Angle Formulas

Same idea in other shifts

Asked 5× in all

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8 Jan 2020, Shift 2 · Q75If $\frac{\sqrt{2}\sin\alpha}{\sqrt{1 + \cos 2\alpha}} = \frac{1}{7}$ and $\sqrt{\frac{1 - \cos 2\beta}{2}} = \frac{1}{\sqrt{10}}$ ,…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.