Cho hai hàm số
\[f,g:\left[ -a,a \right]\to \mathbb{R},f\left( x \right)=\sqrt{a-\sqrt{{{a}^{2}}-{{x}^{2}}}},g\left( x \right)=\sqrt{a+\sqrt{{{a}^{2}}-{{x}^{2}}}},\]
Trong đó $a>0$

Chứng minh rằng
1)
\[f\left( x \right)g\left( y \right)+g\left( x \right)f\left( y \right)\ge \left| x \right|+\left| y \right|\text{ }\forall x,y\in \left[ -a,a \right]\,\,;\]

2)
\[f\left( x \right)f\left( y \right)+g\left( x \right)g\left( y \right)\ge \left| x \right|+\left| y \right|,\text{ }\forall x,y\in \left[ -a,a \right]\,\,\]