Question

The value of $\begin{vmatrix}\sin 10^{\circ} & -\cos 10^{\circ} \\ \sin 80^{\circ} & \cos 80^{\circ}\end{vmatrix}$ is

• A. $-1$
• B. 1
• C. 2
• D. 0

Answer 1

Answer: (B)

Consider, $\begin{vmatrix}\sin 10^{\circ} & -\cos 10^{\circ} \\ \sin 80^{\circ} & \cos 80^{\circ}\end{vmatrix}$
$=\sin 10^{\circ} \cos 80^{\circ}+\sin 80^{\circ} \cos 10^{\circ}$
$=\sin \left(10^{\circ}+80^{\circ}\right)$
$[\because \sin (A+B)=\sin A \cos B+\cos A \sin B]$
$=\sin \left(90^{\circ}\right)=1 \left(\because \sin 90^{\circ}=1\right)$