Let fx=sin2x−2+cos2xcos2x2+sin2xcos2xcos2xsin2xcos2x1+cos2x, x∈0,π. Then the maximum value of fx is equal to _______

Applying R1→R1−R2, R2→R2−R3fx=−2−2020−1sin2xcos2x1+cos2x=4+2cos2xMax.value =4+2=6

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$Let f (x)$ $= |\begin{matrix} \sin^{2} x & - 2 + \cos^{2} x & \cos 2 x \\ 2 + \sin^{2} x & \cos^{2} x & \cos 2 x \\ \sin^{2} x & \cos^{2} x & 1 + \cos 2 x \end{matrix}|,$ $x \in [0, π] .$ Then the maximum value of $f (x)$ is equal to _______

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answer is 6.

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Applying $R_{1} \to R_{1} - R_{2}, R_{2} \to R_{2} - R_{3}$

$f (x) =$ $|\begin{matrix} - 2 & - 2 & 0 \\ 2 & 0 & - 1 \\ \sin^{2} x & \cos^{2} x & 1 + \cos 2 x \end{matrix}|$ $= 4 + 2 \cos 2 x$

Max.value =4+2 $= 6$

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