Read the two statements and choose the correct option.

I. $\cot^{-1} 0$ is defined, and equals $\frac{\pi}{2}$.

II. $\operatorname{cosec}^{-1} \frac{1}{2}$ is defined, and equals $\frac{\pi}{6}$.

Explanation

1. 01

   I: $\cot^{-1}$ is defined on all of $\mathbb{R}$, and $\cot \frac{\pi}{2} = 0$ with $\frac{\pi}{2}$ in $(0, \pi)$. True.

2. 02

   II: $\operatorname{cosec}^{-1}$ needs $\lvert x \rvert \ge 1$, and $\frac{1}{2}$ lies in $(-1, 1)$; $\frac{\pi}{6}$ is $\operatorname{cosec}^{-1} 2$. False.