1. The problem is to evaluate the expression $2 \tan(\sin^{-1}(-1))$. 2. Recall that $\sin^{-1}(x)$ is the inverse sine function, which returns an angle $\theta$ such that $\sin(\theta) = x$ and $\theta$ is in the range $[-\frac{\pi}{2}, \frac{\pi}{2}]$. 3. Since $\sin^{-1}(-1)$ means the angle whose sine is $-1$, we know $\sin(-\frac{\pi}{2}) = -1$. Therefore, $\sin^{-1}(-1) = -\frac{\pi}{2}$. 4. Substitute this back into the expression: $$2 \tan\left(-\frac{\pi}{2}\right)$$ 5. The tangent function $\tan(\theta)$ is $\frac{\sin(\theta)}{\cos(\theta)}$. At $\theta = -\frac{\pi}{2}$, $\cos(-\frac{\pi}{2}) = 0$, so $\tan(-\frac{\pi}{2})$ is undefined (it tends to $-\infty$ or $+\infty$ depending on the direction). 6. Therefore, the expression $2 \tan(\sin^{-1}(-1))$ is undefined because $\tan(-\frac{\pi}{2})$ is undefined. Final answer: The expression is undefined because $\tan\left(\sin^{-1}(-1)\right) = \tan\left(-\frac{\pi}{2}\right)$ is undefined.