9.47 Try to find the maximum value of the following expression:
$$
x \sqrt{1-y^{2}}+y \sqrt{1-x^{2}} .
$$
［Solution］By Cauchy-Schwarz inequality, we have
$$
\left|x \sqrt{1-y^{2}}+y \sqrt{1-x^{2}}\right|^{2} \leqslant\left(x^{2}+y^{2}\right)\left(2-x^{2}-y^{2}\right) .
$$

Using the AM-GM inequality, we get
$$
\left|x \sqrt{1-y^{2}}+y \sqrt{1-x^{2}}\right| \leqslant \frac{x^{2}+y^{2}+2-x^{2}-y^{2}}{2}=1 \text {. }
$$

If $x=\frac{1}{2}, y=\frac{\sqrt{3}}{2}$, then
$$
x \sqrt{1-y^{2}}+y \sqrt{1-x^{2}}=1 .
$$

Therefore, the maximum value sought is 1 .