The teacher hasn't uploaded a solution for this question yet.
The graph of an inverse trigonometric function is defined by its specific domain and range. For the given options, we observe the behavior of the function as $x$ approaches infinity and the values it takes near the origin.
The function $y = \tan^{-1}x$ is defined for all real numbers $x \in (-\infty, \infty)$ and its range is $(-\pi/2, \pi/2)$. The graph passes through the origin $(0,0)$ and is strictly increasing. The functions $y = \cos^{-1}x$, $y = \sec^{-1}x$, and $y = \text{cosec}^{-1}x$ have restricted domains (e.g., $[-1, 1]$ for $\cos^{-1}x$ and $(-\infty, -1] \cup [1, \infty)$ for $\sec^{-1}x$ and $\text{cosec}^{-1}x$), which do not match the continuous curve passing through the origin typically associated with $\tan^{-1}x$.
Based on the standard graphical representation of inverse trigonometric functions in the CBSE curriculum, the curve passing through the origin with horizontal asymptotes at $y = \pi/2$ and $y = -\pi/2$ corresponds to $y = \tan^{-1}x$.
Final Answer: C
AI generated content. Review strictly for academic accuracy.