Question

The value of determinant
$\left|\begin{array}{ccc}{\sin }^{2}13^{\circ }& {\sin }^{2}77^{\circ }& \tan 135^{\circ }\\ {\sin }^{2}77^{\circ }& \tan 135^{\circ }& {\sin }^{2}13^{\circ }\\ \tan 135^{\circ }& {\sin }^{2}13^{\circ }& {\sin }^{2}77^{\circ }\end{array}\right|$ is

• A. -1
• B. 0
• C. 1
• D. 2

Answer 1

Answer: (B)

$\left|\begin{array}{ccc}{\sin }^{2}13^{\circ }& {\cos }^{2}13^{\circ }& -1\\ {\cos }^{2}13^{\circ }& -1& {\sin }^{2}13^{\circ }\\ -1& {\sin }^{2}13^{\circ }& {\cos }^{2}13^{\circ }\end{array}\right|$
$=\left|\begin{array}{ccc}0& {\cos }^{2}13^{\circ }& -1\\ 0& -1& {\sin }^{2}13^{\circ }\\ 0& {\sin }^{2}13^{\circ }& {\cos }^{2}13^{\circ }\end{array}\right|=0$
Applying $C_1\to C_1+C_2+C_3$