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Question

Let f(x)=∣∣ ∣ ∣∣1+sin2xcos2x4sin2xsin2x1+cos2x4sin2xsin2xcos2x1+4sin2x∣∣ ∣ ∣∣, then the maximum value of f(x)=

A
2
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B
4
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C
6
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D
8
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Solution

The correct option is B 6
f(x)=∣ ∣ ∣1+sin2xcos2x4sin2xsin2x1+cos2x4sin2xsin2xcos2x1+4sin2x∣ ∣ ∣
R1R1R2
f(x)=∣ ∣ ∣110sin2x1+cos2x4sin2xsin2xcos2x1+4sin2x∣ ∣ ∣
R2R2R3
f(x)=∣ ∣ ∣110011sin2xcos2x1+4sin2x∣ ∣ ∣
1+4sin2x+cos2x+sin2x
2+4sin2x
MAximum value is attained when sin2x is max
sin2x=1
Maximum value=2+4=6

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