Read the two statements and choose the correct option.

I. $\sin^{-1} x + \cos^{-1} x = \frac{\pi}{2}$ for every $x$ with $\lvert x \rvert \le 1$.

II. $\sec^{-1} x + \operatorname{cosec}^{-1} x = \frac{\pi}{2}$ for every $x$ with $\lvert x \rvert \ge 1$.

Explanation

1. 01

   I: if $\sin^{-1} x = \theta$, then $\cos\left(\frac{\pi}{2} - \theta\right) = x$ with $\frac{\pi}{2} - \theta$ in $[0, \pi]$, so $\cos^{-1} x = \frac{\pi}{2} - \theta$. True.

2. 02

   II: $\sec^{-1} x = \cos^{-1} \frac{1}{x}$ and $\operatorname{cosec}^{-1} x = \sin^{-1} \frac{1}{x}$, and $\frac{1}{x}$ is in $[-1, 1]$; so II is I applied to $\frac{1}{x}$. True.