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

# Maximum value of the expression $\left|\begin{array}{ccc}1+{\mathrm{sin}}^{2}\mathrm{x}& {\mathrm{cos}}^{2}\mathrm{x}& 4\mathrm{sin}2\mathrm{x}\\ {\mathrm{sin}}^{2}\mathrm{x}& 1+{\mathrm{cos}}^{2}\mathrm{x}& 4\mathrm{sin}2\mathrm{x}\\ {\mathrm{sin}}^{2}\mathrm{x}& {\mathrm{cos}}^{2}\mathrm{x}& 1+4\mathrm{sin}2\mathrm{x}\end{array}\right|=$

1. A

4

2. B

6

3. C

2

4. D

-2

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### Solution:

Applying ${C}_{1}\to {C}_{1}+{C}_{2}⇒∆=\left|\begin{array}{ccc}2& {\mathrm{cos}}^{2}x& 4\mathrm{sin}2x\\ 2& 1+{\mathrm{cos}}^{2}x& 4\mathrm{sin}2x\\ 1& {\mathrm{cos}}^{2}x& 1+4\mathrm{sin}2x\end{array}\right|$

Applying ${\mathrm{R}}_{2}\to {\mathrm{R}}_{2}-{\mathrm{R}}_{1}$ and ${\mathrm{R}}_{3}\to {\mathrm{R}}_{3}-{\mathrm{R}}_{1}$

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