Question

If the determinant $\left|\begin{array}{ccc}cos2x& si{n}^{2}x& cos4x\\ si{n}^{2}x& cos2x& co{s}^{2}x\\ cos4x& co{s}^{2}x& cos2x\end{array}\right|$ is expanded in powers of $sinx$ then the negative of constant term in the expansion is ...............

• A. $1$
• B. $-1$
• C. $-2$
• D. $0$

Answer 1

The correct option is A $1$

Let $\left|\begin{array}{ccc}\cos 2x& {\sin }^{2}x& \cos 4x\\ {\sin }^{2}x& \cos 2x& {\cos }^{2}x\\ \cos 4x& {\cos }^{2}x& \cos 2x\end{array}\right|=a_0+a_1\sin x+a_2{\sin }^{2}x+...$
Put $x=0$

$\left|\begin{array}{ccc}1& 0& 1\\ 0& 1& 1\\ 1& 1& 1\end{array}\right|=a_0$

$\Rightarrow a_0=-1$