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JEE Main 201912 AprilMorning Shift
Exam
JEE Main
Year
2019
Date
12 April
Shift
Morning Shift
Subject
Mathematics
Chapter
Trigonometric Equations

JEE Main 2019 · 12 April · Morning Shift · Mathematics · Trigonometric Equations

The number of solutions of the equation 1 + ^ 4 x = ^ 2 3x, x ∈ [-...

The number of solutions of the equation 1+sin⁡4x=cos⁡23x,x∈[−5π2,5π2]1 + \sin^{4}x = \cos^{2}3x, x \in \left[- \dfrac{5\pi}{2}, \dfrac{5\pi}{2}\right] is:

Options

  1. A55
  2. B77
  3. C33
  4. D44

Correct answer

A. 55

Step-by-step solution

The given trigonometric equation can be written as
1−cos⁡23x+sin⁡4x=01 - \cos^{2}3x + \sin^{4}x = 0

⇒sin⁡23x+sin⁡4x=0⇒ \sin^{2}3x + \sin^{4}x = 0

⇒sin⁡3x=0⇒ \sin 3x = 0 and sin⁡x=0\sin x = 0 ,x∈[−5π2,5π2], x \in \left[- \dfrac{5\pi}{2}, \dfrac{5\pi}{2}\right]

In given interval sin⁡x=0\sin x = 0 at x=−2π,−π,0,π,2πx = - 2\pi, - \pi, 0, \pi, 2\pi and these values are also satisfied by sin⁡3x=0.\sin 3x = 0 .
Hence total number of solutions is 5.5 .

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