Read the two statements and choose the correct option.

I. $\tan x$ is strictly increasing on $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$.

II. $\cot x$ is strictly increasing on $(0, \pi)$.

Explanation

1. 01

   I: $\frac{d}{dx}\tan x = \sec^{2} x > 0$ on $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$. True.

2. 02

   II: $\frac{d}{dx}\cot x = -\operatorname{cosec}^{2} x < 0$, so $\cot x$ is strictly decreasing on $(0, \pi)$. False.