Read the two statements and choose the correct option.

I. The curves $y = \sin^{-1} x$ and $y = \cos^{-1} x$ are mirror images of each other in the line $y = x$.

II. The curves $y = \tan^{-1} x$ and $y = \cot^{-1} x$ are mirror images of each other in the line $y = \frac{\pi}{4}$.

Explanation

1. 01

   I: the mirror image of $y = \sin^{-1} x$ in $y = x$ is $y = \sin x$, $-\frac{\pi}{2} \le x \le \frac{\pi}{2}$, which runs over $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$, not $[-1, 1]$. False.

2. 02

   II: $\cot^{-1} x = \frac{\pi}{2} - \tan^{-1} x$, so at each $x$ the two heights are equally far above and below $\frac{\pi}{4}$. True.