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JEE Main 20163 April
Exam
JEE Main
Year
2016
Date
3 April
Subject
Mathematics
Chapter
Trigonometric Equations

JEE Main 2016 · 3 April · Mathematics · Trigonometric Equations

If 0 ≤ x < 2π, then the number of real values of x, which satisfy...

If 0≤x<2π,0 \le x < 2\pi, then the number of real values of x,x, which satisfy the equation cos⁡x+cos⁡2x+cos⁡3x+cos⁡4x=0,\cos x + \cos 2x + \cos 3x + \cos 4x = 0, is

Options

  1. A77
  2. B99
  3. C33
  4. D55

Correct answer

A. 77

Step-by-step solution

2cos⁡2xcosx+2cos⁡3xcosx=02\cos 2xcosx + 2\cos 3xcosx = 0

⇒⇒ 2cos⁡x(cos⁡2x+cos⁡3x)=02\cos x\left(\cos 2x + \cos 3x\right) = 0

2cos⁡x2cos5x2cosx2=02\cos x2cos\dfrac{5x}{2}cos\dfrac{x}{2} = 0

x=π2,3π2,π,π5,3π5,7π5,9π5x = \dfrac{\pi}{2}, \dfrac{3\pi}{2}, \pi, \dfrac{\pi}{5}, \dfrac{3\pi}{5}, \dfrac{7\pi}{5}, \dfrac{9\pi}{5}

77Solutions.
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