JEE Main 2020MathematicsTrigonometric Ratios & IdentitiesMediumNumerical

JEE Main 2020 — Trigonometric Ratios & Identities Question with Solution

JEE Main 2020 (08 Jan Shift 2)

Question

If 2sinα1+cos2α=17 and 1-cos2β2=110, α, β∈0,π2, then tanα+2β, is equal to

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Correct answer
1

Step-by-step explanation

Given,

2sinα1+cos2α=17 and 1-cos2β2=110, α, β∈0,π2

Now using cos2θ=2cos2θ-1=1-2sin2θ, we can write

2sin⁡α2cos⁡α=17 and 2sin⁡β2=110


tan⁡α=17 and sin⁡β=110 or tan⁡β=13
tan2β=2tan⁡β1-tan2⁡β=2.131-19=34
tan⁡α+2β=tanα+tan2β1-tanαtan⁡2β=17+341-17·34=4+21282528=1

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About this question

This is a previous-year question from JEE Main 2020, 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.