Evaluate $\left|\begin{array}{cc}2 \cos \theta & -2 \sin \theta \\ \sin \theta & \cos \theta\end{array}\right|$

Solution:

After finding determinant we will get a trigonometric identity.
$\begin{array}{l}
2 \cos ^{2} \theta+2 \sin ^{2} \theta \\
=2 \\
\because \sin ^{2} \theta+\cos ^{2} \theta=1
\end{array}$