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(C) To find the constant term $a_0$ in the expansion of the determinant,we set $x = 0$.Substituting $x = 0$ into the determinant:$\cos(2 	imes 0) = \

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$-1$

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(C) To find the constant term $a_0$ in the expansion of the determinant,we set $x = 0$.Substituting $x = 0$ into the determinant:$\cos(2 	imes 0) = \cos(0) = 1$$\sin^2(0) = 0$$\cos(4 	imes 0) = \cos(0) = 1$$\cos^2(0) = 1$The determinant becomes:$\Delta = \left| \begin{array}{ccc} 1 & 0 & 1 \ 0 & 1 & 1 \ 1 & 1 & 1 \end{array} ight|$Expanding along the first row:$\Delta = 1(1 	imes 1 - 1 	imes 1) - 0(0 	imes 1 - 1 	imes 1) + 1(0 	imes 1 - 1 	imes 1)$$\Delta = 1(0) - 0(-1) + 1(-1)$$\Delta = 0 + 0 - 1 = -1$Since the expansion is $a_0 + a_1 \sin x + a_2 \sin^2 x + \dots$,setting $x = 0$ gives $a_0 = -1$.

If $\left| \begin{array}{ccc} \cos 2x & \sin^2 x & \cos 4x \\ \sin^2 x & \cos 2x & \cos^2 x \\ \cos 4x & \cos^2 x & \cos 2x \end{array} \right| = a_0 + a_1 \sin x + a_2 \sin^2 x + \dots$,then $a_0$ is equal to:

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