Question

$\left|\begin{array}{ccc}si{n}^{2}x& co{s}^{2}x& 1\\ co{s}^{2}x& si{n}^{2}x& 1\\ -10& 12& 2\end{array}\right|=$

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

Answer 1

Answer: (A)

$0$

Let $A=\left|\begin{array}{ccc}{\sin }^{2}x& {\cos }^{2}x& 1\\ {\cos }^{2}x& {\sin }^{2}x& 1\\ -10& 12& 2\end{array}\right|$
So, By column trasformation on determinant
$C_1\to C_1+C_2$
$A=\left|\begin{array}{ccc}1& {\cos }^{2}x& 1\\ 1& {\sin }^{2}x& 1\\ 2& 12& 2\end{array}\right|$
then $C_1\to C_1-C_3$
$A=\left|\begin{array}{ccc}0& {\cos }^{2}x& 1\\ 0& {\sin }^{2}x& 1\\ 0& 12& 1\end{array}\right|$
$\Rightarrow A=0$