JEE Main 2019MathematicsTrigonometric EquationsMediumMCQ

JEE Main 2019 — Trigonometric Equations Question with Solution

JEE Main 2019 (10 Jan Shift 1)

Question

The sum of all values of  θ∈0, π2 satisfying sin22θ+cos42θ=34 is

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Show full solutionCorrect option: A
Correct answer
Aπ2

Step-by-step explanation

Given sin22θ+cos42θ=34

Using sin2x+cos2x=1, we get

⇒1-cos22θ+cos42θ=34

Let cos22θ=t

⇒t2-t+14=0

⇒t-122=0

⇒t=12

⇒cos22θ=12

⇒2cos22θ-1=0

Using cos2A=2cos2A-1, we get

⇒cos4θ=0

If cosx=0, then x=2n+1π2, n∈Z.

⇒4θ=2n+1π2

⇒θ=2n+1π8

⇒θ=π8, 3π8 ∈ 0, π2

Hence, the sum of the values of θ is π8+3π8=π2.

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About this question

This is a previous-year question from JEE Main 2019, covering the Trigonometric Equations 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.