JEE Main 2016MathematicsTrigonometric Ratios & IdentitiesMediumMCQ

JEE Main 2016 — Trigonometric Ratios & Identities Question with Solution

JEE Main 2016 (09 Apr Online)

Question

If m and M are the minimum and the maximum values of 4+12sin2⁡2x-2cos4⁡x, x ∈R, then M-m is equal to:

Choose an option

Show full solutionCorrect option: B
Correct answer
B94

Step-by-step explanation

Given expression is 4+12sin2⁡2x-2cos4⁡x

=  4+21-cos2⁡xcos2⁡x-2cos4⁡x

Creating perfect squares, we get

=-4 cos2⁡x-142-1716 

Since, 0 ≤cos2⁡x ≤1

⇒ -14 ≤cos2⁡x-14 ≤34

⇒ 0 ≤cos2⁡x-142 ≤916

⇒ -1716 ≤cos2⁡x-142-1716 ≤916-1716

⇒ 174 ≥-4 cos2⁡x-142-1716 ≥2

⇒ M=174 and m=2
⇒ M-m=174-2=94

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About this question

This is a previous-year question from JEE Main 2016, 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.