1. The problem asks if $\tan^{-1}(1)$ equals $\frac{\pi}{4}$.\n\n2. The function $\tan^{-1}(x)$, also called arctangent, gives the angle whose tangent is $x$.\n\n3. We know from trigonometry that $\tan\left(\frac{\pi}{4}\right) = 1$.\n\n4. Since $\tan^{-1}$ is the inverse of $\tan$ on its principal domain $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$, it follows that $\tan^{-1}(1) = \frac{\pi}{4}$.\n\n5. Therefore, the statement is true: $\tan^{-1}(1)$ means $\frac{\pi}{4}$.