Question

The value of $\left|\begin{array}{cc}\sin 10^{\circ }& -\cos 10^{\circ }\\ \sin 80^{\circ }& \cos 80^{\circ }\end{array}\right|$ is

• A. $-1$
• B. 1
• C. 2
• D. 0

Answer 1

Answer: (B)

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