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Question

Let f(x)=∣ ∣ ∣6cos2xcos2x4sin2xsin2x5+cos2x4sin2xsin2xcos2x5+4sin2x∣ ∣ ∣, where xR. If M and m denote the maximum and the minimum values of f respectively, then the value of Mm is

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Solution

Given f(x)=∣ ∣ ∣6cos2xcos2x4sin2xsin2x5+cos2x4sin2xsin2xcos2x5+4sin2x∣ ∣ ∣

Applying R1R1R2
f(x)=∣ ∣ ∣550sin2x5+cos2x4sin2xsin2xcos2x5+4sin2x∣ ∣ ∣

Applying R2R2R3
f(x)=∣ ∣ ∣550055sin2xcos2x5+4sin2x∣ ∣ ∣

=25∣ ∣ ∣110011sin2xcos2x5+4sin2x∣ ∣ ∣

f(x)=150+100sin2x
M=150+100=250 and m=150100=50

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