JEE Main 2019MathematicsTrigonometric Ratios & IdentitiesEasyMCQ

JEE Main 2019 — Trigonometric Ratios & Identities Question with Solution

JEE Main 2019 (08 Apr Shift 1)

Question

If cosα+β=35 ,sin⁡(α-β)=513 and 0<α,β<π4, then tan⁡2α is equal to:

Choose an option

Show full solutionCorrect option: D
Correct answer
D6316

Step-by-step explanation

cosα+β=35⇒tanα+β=43

sin(α-β)=513⇒tan(α-β)=512

Now,

tan2α=tanα+β+α-β

            =tan(α+β)+tan(α-β)1-tan(α+β)tan(α-β)

            =43+5121-43×512=6316

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About this question

This is a previous-year question from JEE Main 2019, 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.