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JEE Main 20199 JanuaryEvening Shift
Exam
JEE Main
Year
2019
Date
9 January
Shift
Evening Shift
Subject
Mathematics
Chapter
Trigonometric Equations

JEE Main 2019 · 9 January · Evening Shift · Mathematics · Trigonometric Equations

If 0 ≤ x < (π)/(2), then the number of values of x for which x - 2x...

If 0≤x<π2,0 \le x < \dfrac{\pi}{2}, then the number of values of xx for which sin⁡x−sin⁡2x+sin⁡3x=0,\sin x - \sin 2x + \sin 3x = 0, is:

Options

  1. A44
  2. B33
  3. C22
  4. D11

Correct answer

C. 22

Step-by-step solution

sin⁡x−sin⁡2x+sin⁡3x=0\sin x - \sin 2x + \sin 3x = 0

⇒sin⁡x+sin⁡3x−sin⁡2x=0⇒ \sin x + \sin 3x - \sin 2x = 0

⇒2sin⁡2x.cos⁡x−sin⁡2x=0⇒ 2\sin 2x . \cos x - \sin 2x = 0

⇒sin⁡2x=0⇒ \sin 2x = 0 or cos⁡x=12\cos x = \dfrac{1}{2}

⇒2x=0⇒ 2x = 0 or x=π3x = \dfrac{\pi}{3}

⇒x=0⇒ x = 0 or x=π3x = \dfrac{\pi}{3}

∴∴ Number of solutions =2= 2

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