Determinants and Trigonometry

Question

If $$ \det \begin{bmatrix} \sin(2x) & \cos^2 x & \cos(4x) \\ \cos^2 x & \cos(2x) & \sin^2 x \\ \cos^4 x & \sin^2 x & \sin(2x) \end{bmatrix} = A + B\sin x + C \sin^2 x + \cdots + Z\sin^n x $$

Then the value of $A$ is??

(a) $\quad -1$ (correct option)

(b) $\quad 1$

(c) $\quad 0$

(d) $\quad 2$

Answer 1

HintWhen you set $x=0$ you get all $\sin$ to be equal to $0$.