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The maximum value of
$$f(x) = \begin{vmatrix} \sin^2 x & 1 + \cos^2 x & \cos 2x \ 1 + \sin^2 x & \cos^2 x & \cos 2x \ \sin^2 x & \cos^2 x & \sin 2x \end{vmatrix}, \quad x \in R \text{ is:}$$
(1) $\sqrt{7}$
(2) $\dfrac{3}{4}$
(3) $\sqrt{5}$
(4) $5$
BETA
