Maximum value of the expression 1+sin2xcos2x4sin2xsin2x1+cos2x4sin2xsin2xcos2x1+4sin2x=

A
4
B
6
C
2
D
-2

Solution:

Applying $C_{1} \to C_{1} + C_{2} \Rightarrow ∆ = |\begin{matrix} 2 & \cos^{2} x & 4 \sin 2 x \\ 2 & 1 + \cos^{2} x & 4 \sin 2 x \\ 1 & \cos^{2} x & 1 + 4 \sin 2 x \end{matrix}|$

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

$\Rightarrow ∆ = |\begin{matrix} 2 & \cos^{2} x & 4 \sin 2 x \\ 0 & 1 & 0 \\ - 1 & 0 & 1 \end{matrix}| \Rightarrow ∆ = 2 (1 - 0) - \cos^{2} x (0 + 0) + 4 \sin 2 x (0 + 1) \Rightarrow ∆ = 2 - 0 + 4 \sin 2 x \Rightarrow ∆ = 2 + 4 \sin 2 x = \Rightarrow m a x i m u m v a l u e o f ∆ = 6$

Maximum value of the expression $|\begin{matrix} 1 + \sin^{2} x & \cos^{2} x & 4 \sin 2 x \\ \sin^{2} x & 1 + \cos^{2} x & 4 \sin 2 x \\ \sin^{2} x & \cos^{2} x & 1 + 4 \sin 2 x \end{matrix}| =$

Solution:

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