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Question

If the maximum and the minimum values of ∣ ∣ ∣1+sin2xcos2x4sin2xsin2x1+cos2x4sin2xsin2xcos2x1+4sin2x∣ ∣ ∣ are M and m respectively, then Mm is

A
2
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B
3
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C
3
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D
2
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Solution

The correct option is B 3
Δ=∣ ∣ ∣1+sin2xcos2x4sin2xsin2x1+cos2x4sin2xsin2xcos2x1+4sin2x∣ ∣ ∣

Applying C1C1+C2, we get
Δ=∣ ∣ ∣2cos2x4sin2x21+cos2x4sin2x1cos2x1+4sin2x∣ ∣ ∣

Applying R2R2R1 and then R3R3R1, we get
Δ=∣ ∣2cos2x4sin2x010101∣ ∣

=2+4sin2x
M=6 and m=2
Hence, Mm=3

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