2. As shown in the figure, $S-A B C$ is a triangular pyramid with three edges mutually perpendicular, and $O$ is a point within the base $A B C$. If $\angle O S A=\alpha, \angle O S B=\beta, \angle O S C=\gamma$, then the range of $\tan \alpha \cdot \tan \beta \cdot \tan \gamma$ is ( ).
A. $[2 \sqrt{2},+\infty)$
B. $(0,2 \sqrt{2})$
C. $[1,2 \sqrt{2}]$
D. $(1,2 \sqrt{2})$
2. Through $O$, construct planes parallel to $S A$, $S B$, and $S C$ intersecting $S A$, $S B$, and $S C$ at $D$, $E$, and $F$, respectively, thus forming a rectangular parallelepiped MFSE-ONDP with $\mathrm{SO}$ as the diagonal.
Given that $\cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma=1$,
and $\sin ^{2} \gamma=\cos ^{2} \alpha+\cos ^{2} \beta \geqslant 2 \cos \alpha \cos \beta$,
$$
\begin{array}{l}
\sin ^{2} \alpha=\cos ^{2} \beta+\cos ^{2} \gamma \geqslant 2 \cos \beta \cos \gamma, \\
\sin ^{2} \beta=\cos ^{2} \alpha+\cos ^{2} \gamma \geqslant 2 \cos \alpha \cos \gamma,
\end{array}
$$

we get $\tan \alpha \tan \beta \tan \gamma \geqslant 2 \sqrt{2}$. Therefore, the answer is $A$.