Question:
Evaluate: $\left|\begin{array}{ll}\cos 15^{\circ} & \sin 15^{\circ} \\ \sin 75^{\circ} & \cos 75^{\circ}\end{array}\right|$
Solution:
$\begin{array}{ll}\mid \cos 15^{\circ} & \sin 15^{\circ} \\ \sin 75^{\circ} & \cos 75^{\circ} \mid\end{array}$
$=\cos 15^{\circ} \cos 75^{\circ}-\sin 15^{\circ} \sin 75^{\circ}$
$=\cos \left(15^{\circ}+75^{\circ}\right) \quad[\because \cos A \cos B-\sin A \sin B=\cos (A+B)]$
$=\cos 90^{\circ}$
$=0$
$\Rightarrow \mid \cos 15^{\circ} \sin 15^{\circ}$
$\sin 75^{\circ} \quad \cos 75^{\circ} \mid=0$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.