JEE Main 2017MathematicsTrigonometric Ratios & IdentitiesMediumMCQ

JEE Main 2017 — Trigonometric Ratios & Identities Question with Solution

JEE Main 2017 (02 Apr)

Question

If 5tan2⁡x-cos2⁡x=2cos⁡ 2x+9, then the value of cos⁡4x is

Choose an option

Show full solutionCorrect option: D
Correct answer
D-79

Step-by-step explanation

51-cos⁡2x1+cos⁡2x-1+cos⁡2x2=2cos⁡2x+9

Let, cos⁡2x=y

 ∴    5(1−y1+y−1+y2)=2y+9

⇒ 5-y2-4y+1=4y2+22y+18

⇒ 9y2+42y+13=0

⇒ y=-13 or y=-133 (Not possible)

Now, cos⁡4x=2cos2⁡2x-1

⇒ cos⁡4x=2-132-1

⇒ cos⁡4x=-79

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About this question

This is a previous-year question from JEE Main 2017, 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.