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AP EAMCET · Maths · Trigonometric Equations

The number of solutions of the equation \(4 \cos 2 \theta \cos 3 \theta=\sec \theta\) in the interval \([0,2 \pi]\) is

  1. A \(12\)
  2. B \(8\)
  3. C \(16\)
  4. D \(4\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(12\)

Step-by-step Solution

Detailed explanation

\(4 \cos 2 \theta \cos 3 \theta \cos \theta = 1\), \(\cos \theta \neq 0\) \(2 \cos 2 \theta (\cos 4 \theta + \cos 2 \theta) = 1\) \(\cos 6 \theta + \cos 4 \theta + \cos 2 \theta = 0\) \(\cos 4 \theta (2 \cos 2 \theta + 1) = 0\) If \(\cos 4 \theta = 0\):…