Determinants Matrices Question 59
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
Options:
A) $ -1 $
B) $ 0 $
C) $ 1 $
D) $ 2 $
Show Answer
Answer:
Correct Answer: B
Solution:
- [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\to C_1+C_2+C_3 $
BETA
