Q15 / 83 · NTA Abhyas (JEE Main) 2020 · Mathematics · Trigonometric Equations

The number of solutions in the interval 0,π of the equation sin3⁡xcos⁡3x+sin⁡3xcos3⁡x=0 is equal to

  • A
    7
  • B
    6
  • Correct answer
    C
    5
  • D
    4

Solution

The given equation can be written as
3sin⁡x-sin⁡3x4cos⁡3x+sin⁡3x3cos⁡x+cos⁡3x4
sin⁡xcos3x⁡+cos⁡xsin⁡3x=0
So, sin⁡x+3x=0⇒sin⁡4x=0
⇒x=nπ4, n∈Z.
⇒x=0,π4,π2,3π4,π
⇒5 solutions

Hence, the correct answer is option: 'C'.

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