Question
Download Solution PDFThe maximum values of 1 − 4 sin2 x cos2 x is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
-1 ≤ sin θ ≤ 1
0 ≤ sin2 θ ≤ 1
sin 2 θ = 2 sin θ cos θ
Calculation
We have to find the maximum value of 1 − 4 sin2 x cos2 x
Let f(x) = 1 − 4 sin2 x cos2 x
= 1 – (2 sin x cos x)2
= 1 – sin2 2x (∵sin 2θ = 2 sin θ cos θ)
For maximum value of f(x), sin 2x should be minimum
As we know that,
Minimum value of sin2 θ is 0
Therefore, Maximum value of f(x) = 1 – 0 = 1
Last updated on Jun 20, 2025
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