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

Question

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

Aicharya · Accepted Answer

Given, $ \begin{aligned} & \frac{2 an x}{1- an ^2 x}>0 \ & an 2 x>0 \end{aligned} $ Since, $\quad 0 < 2 x < \frac{\pi}{2} \quad\left[\because an 2 x ight.$ is the in $\left.Q_1 ight]$ $ \begin{array}{ll} \Rightarrow & 0 < x < \frac{\pi}{4} \ herefore & 0 < x < \frac{\pi}{4} ext { as } x \in\left(0, \frac{\pi}{2} ight) \end{array} $ Hence, option (3) is correct

For the value of $\frac{2 \tan (x)}{1-\tan ^2(x)}$ to be positive, find values of $x$, such that $x…

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