Assertion (A): For $0 < x \le 1$, the curve $y = \sin^{-1} x$ lies below the line $y = x$.

Reason (R): The curve $y = \sin^{-1} x$ is the mirror image of $y = \sin x$, $-\frac{\pi}{2} \le x \le \frac{\pi}{2}$, in the line $y = x$.

Explanation

1. 01

   R is true: $\sin^{-1}$ undoes $\sin$ on its branch, which swaps $x$ and $y$.

2. 02

   For $0 < x \le \frac{\pi}{2}$, $\sin x < x$, so $y = \sin x$ lies below $y = x$ and its mirror image lies above; for example $\sin^{-1} 1 = \frac{\pi}{2} > 1$. A is false.