Question:
Write the value of $\left|\begin{array}{cc}\sin 20^{\circ} & -\cos 20^{\circ} \\ \sin 70^{\circ} & \cos 70^{\circ}\end{array}\right|$.
Solution:
Let $\Delta=\mid \sin 20^{\circ} \quad-\cos 20^{\circ}$
$\sin 70^{\circ} \quad \cos 70^{\circ}$
$=\sin 20^{\circ} \cos 70^{\circ}+\cos 20^{\circ} \sin 70^{\circ}$
$=\sin \left(20^{\circ}+70^{\circ}\right) \quad[$ trignometric identity $]$
$=\sin 90^{\circ}$
$=1$