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AP EAMCET · Maths · Trigonometric Equations

The number of solutions of the equation \(\sec x \cos 5 x+1=0\) in the interval \([0,2 \pi]\) is

  1. A \(5\)
  2. B \(8\)
  3. C \(10\)
  4. D \(12\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(8\)

Step-by-step Solution

Detailed explanation

\(\sec x \cos 5 x+1=0\) \(\frac{\cos 5x}{\cos x} = -1 \implies \cos 5x = -\cos x \implies \cos 5x = \cos(\pi - x)\) \(5x = 2n\pi \pm (\pi - x)\), where \(\cos x \neq 0\) Case 1: \(5x = 2n\pi + \pi - x \implies 6x = (2n+1)\pi \implies x = \frac{(2n+1)\pi}{6}\) For…