Question

Evaluate the following determinant:

\[\begin{vmatrix}\cos \theta & - \sin \theta \\ \sin \theta & \cos \theta\end{vmatrix}\]

Answer 1

\[∆ = \cos^2 \theta - \left( - \sin^2 \theta \right)\]
\[ = \cos^2 \theta + \sin^2 \theta = 1\]