Example 2. Given the sequence $\left\{\mathrm{a}_{\mathrm{n}}\right\}$, the sum of the first $\mathrm{n}$ terms is $\mathrm{S}_{\mathrm{n}}$ $=1-\sin ^{2 n} \alpha$, try to find $a_{n} . \quad(\alpha \neq k \pi)$
$$
\begin{array}{l}
n \geqslant 2 \text { when } a_{n}=S_{n}-S_{n-1} \\
=\cos ^{2} \alpha \sin ^{2}(n-1) \alpha ; \\
n=1 \text { when, } a_{1}=S_{1}=1-\sin ^{2} \alpha=\cos ^{2} \alpha \\
\quad=\cos ^{2} \alpha \sin ^{2(1-1) \alpha}
\end{array}
$$
$\therefore$ The general term formula of the sequence is:
$$
a_{n}=\cos ^{2} \alpha \sin ^{2(n-1)} \alpha .
$$