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TS EAMCET · Maths · Trigonometric Equations

If \(x \in(-\pi, \pi)\) then the number of solutions of the equation \(2 \sin x \sin 3 x \sin 5 x+\sin 5 x \cos 4 x=0\) is

  1. A 14
  2. B 12
  3. C 13
  4. D 9
Verified Solution

Answer & Solution

Correct Answer

(C) 13

Step-by-step Solution

Detailed explanation

\(2 \sin x \sin 3 x \sin 5 x+\sin 5 x \cos 4 x=0\) \(\sin 5x (2 \sin x \sin 3 x + \cos 4 x) = 0\) \(\sin 5x (\cos(x-3x) - \cos(x+3x) + \cos 4x) = 0\) \(\sin 5x (\cos 2x - \cos 4x + \cos 4x) = 0\) \(\sin 5x \cos 2x = 0\) Case 1:…