JEE Main 2022MathematicsTrigonometric Ratios & IdentitiesMediumMCQ

JEE Main 2022 — Trigonometric Ratios & Identities Question with Solution

JEE Main 2022 (28 Jun Shift 2)

Question

If cotα=1 and secβ=-53, where π<α<3π2 and π2<β<π, then the value of tanα+β and the quadrant in which α+β lies, respectively are

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Show full solutionCorrect option: A
Correct answer
A-17 and IVth quadrant

Step-by-step explanation

Given,

cotα=1,secβ=-53

So, cosβ=-35,tanβ=-43 and tanα=1

Now using formula tanα+β=tanα+tanβ1-tanαtanβ

⇒tanα+β=1-431+43×1=-17 

We know that tanθ is negative in 2nd & 4th  quadrant but as π<α<3π2, so α+β will lie in IVth quadrant.

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About this question

This is a previous-year question from JEE Main 2022, covering the Trigonometric Ratios & Identities chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.