Question

The value of determinant
$\begin{vmatrix}\sin ^{2} 13^{\circ} & \sin ^{2} 77^{\circ} & \tan 135^{\circ} \\ \sin ^{2} 77^{\circ} & \tan 135^{\circ} & \sin ^{2} 13^{\circ} \\ \tan 135^{\circ} & \sin ^{2} 13^{\circ} & \sin ^{2} 77^{\circ}\end{vmatrix}$ is

• A. -1
• B. 0
• C. 1
• D. 2

Answer 1

Answer: (B)

$\begin{vmatrix}\sin ^{2} 13^{\circ} & \cos ^{2} 13^{\circ} & -1 \\ \cos ^{2} 13^{\circ} & -1 & \sin ^{2} 13^{\circ} \\ -1 & \sin ^{2} 13^{\circ} & \cos ^{2} 13^{\circ}\end{vmatrix}$
$=\begin{vmatrix}0 & \cos ^{2} 13^{\circ} & -1 \\ 0 & -1 & \sin ^{2} 13^{\circ} \\ 0 & \sin ^{2} 13^{\circ} & \cos ^{2} 13^{\circ}\end{vmatrix}=0$
Applying $C _{1} \rightarrow C _{1}+ C _{2}+ C _{3}$