1. If $a_{n}=\left\{\begin{array}{cc}1, & n \text { is odd, } \\ -1, & n \text { is even, }\end{array} a_{n}\right.$ can be represented by a unified formula, which is $a_{n}=(-1)^{n+1}$. Given $\sin \frac{\pi}{8}=\frac{1}{2} \sqrt{2-\sqrt{2}}, \cos \frac{\pi}{8}=\frac{1}{2} \sqrt{2+\sqrt{2}}$. Then these two formulas can be represented by a unified formula as $\qquad$
$\begin{array}{l}\text { II. } 1 \cdot \sin \left[\frac{1+(-1)^{n}}{2} \cdot \frac{\pi}{2}+\frac{\pi}{8}\right] \\ =\frac{1}{2} \sqrt{2+(-1)^{n} \sqrt{2}} .\end{array}$