[填空题]
In a triangle $\mathrm{ABC}, \mathrm{AB}=2 \mathrm{~cm}$, $\mathrm{CBA}=\frac{\pi}{4}$ and $\mathrm{BA} \mathrm{A}= x $ .
1. Show that $\mathrm{AC}=\frac{2}{\cos x+\sin x}$ .
2. Given that AC has a minimum value, find the value of x for which this occurs.
