Solution:
After finding determinant we will get a trigonometric identity.
$\begin{array}{l}
\cos ^{2} \alpha+\sin ^{2} \alpha \\
=1
\end{array}$
$\because \sin ^{2} \theta+\cos ^{2} \theta=1$
Evaluate $\left|\begin{array}{cc}\cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha\end{array}\right|$
Evaluate $\left|\begin{array}{cc}\cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha\end{array}\right|$