Question

$\left| \begin{matrix} \sin^{2}x & \cos^{2}x & 1 \ \cos^{2}x & \sin^{2}x & 1 \

• 10 & 12 & 2 \end{matrix} \right| =$

• A. 0
• B. $12\cos^{2}x - 10\sin^{2}x$
• C. $12\sin^{2}x - 10\cos^{2}x - 2$
• D. $10\sin 2x$

Answer 1

Answer: (A)

0

Answer 2

Applying $C_{1} \rightarrow C_{1} + C_{2}$, we get $\left| \begin{matrix} 1 & \cos^{2}x & 1 \\ 1 & \sin^{2}x & 1 \\ 2 & 12 & 2 \end{matrix} \right| = 0$.