7. If $\alpha, \beta, \gamma$ are acute angles, and $\sin ^{2} \alpha+\sin ^{2} \beta+\sin ^{2} \gamma=1$, then the maximum value of $\frac{\sin \alpha+\sin \beta+\sin \gamma}{\cos \alpha+\cos \beta+\cos \gamma}$ is
$\qquad$ .
7. $\frac{\sqrt{2}}{2}$ Detailed Explanation: From $\frac{a^{2}+b^{2}}{2} \geqslant\left(\frac{a+b}{2}\right)^{2} \Rightarrow a+b \leqslant \sqrt{2\left(a^{2}+b^{2}\right)}$,

thus $\sin \alpha+\sin \beta \leqslant \sqrt{2\left(\sin ^{2} \alpha+\sin ^{2} \beta\right)}=\sqrt{2} \cos \gamma$.
Similarly: $\sin \beta+\sin \gamma \leqslant \sqrt{2} \cos \alpha, \sin \gamma+\sin \alpha \leqslant \sqrt{2} \cos \beta$.
Therefore, $2(\sin \alpha+\sin \beta+\sin \gamma) \leqslant \sqrt{2}(\cos \alpha+\cos \beta+\cos \gamma)$, hence $\frac{\sin \alpha+\sin \beta+\sin \gamma}{\cos \alpha+\cos \beta+\cos \gamma} \leqslant \frac{\sqrt{2}}{2}$.