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AP EAMCET · Maths · Trigonometric Ratios & Identities

For the value of \(\frac{2 \tan (x)}{1-\tan ^2(x)}\) to be positive, find values of \(x\), such that \(x \in\left(0, \frac{\pi}{2}\right)\)

  1. A \(\left(0, \frac{\pi}{3}\right)\)
  2. B \(\left(0, \frac{\pi}{6}\right)\)
  3. C \(\left(0, \frac{\pi}{4}\right)\)
  4. D \(\left(0, \frac{\pi}{8}\right)\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\left(0, \frac{\pi}{4}\right)\)

Step-by-step Solution

Detailed explanation

Given, \[ \begin{aligned} & \frac{2 \tan x}{1-\tan ^2 x}>0 \\ & \tan 2 x>0 \end{aligned} \] Since, \(\quad 0 < 2 x < \frac{\pi}{2} \quad\left[\because \tan 2 x\right.\) is the in \(\left.Q_1\right]\)…