Áp dụng BĐT Cô-si:
\(x\sqrt{1-y^2}+y\sqrt{1-x^2}\le\frac{1}{2}\left(x^2+1-y^2\right)+\frac{1}{2}\left(y^2+1-x^2\right)=1\)
Do dấu "=" xảy ra nên:
\(\left\{{}\begin{matrix}x=\sqrt{1-y^2}\\y=\sqrt{1-x^2}\end{matrix}\right.\) \(\Rightarrow x^2+y^2=1\)