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AP EAMCET · Maths · Trigonometric Equations

Find the value of \(\theta\), if \(|\tan \theta|=\tan \theta+\frac{1}{\cos \theta}\) and \(\theta \in[0,2 \pi]-\left\{ \pm \frac{\pi}{2}\right\}\)

  1. A \(\frac{11 \pi}{3}\)
  2. B \(\frac{11 \pi}{6}\)
  3. C \(\frac{13 \pi}{3}\)
  4. D \(\frac{13 \pi}{6}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{11 \pi}{6}\)

Step-by-step Solution

Detailed explanation

If \(\tan \theta \ge 0\): \(\tan \theta = \tan \theta + \frac{1}{\cos \theta} \implies 0 = \frac{1}{\cos \theta}\) (No solution). If \(\tan \theta \(-2\tan \theta = \frac{1}{\cos \theta}\) \(-2\frac{\sin \theta}{\cos \theta} = \frac{1}{\cos \theta}\) \(-2\sin \theta = 1\)…