Задача 52319 sin^(4)x-cos^(4)x<=sqrt(3)/2...

vk193930936

2020-06-10 11:07:36

sin^(4)x-cos^(4)x<=sqrt(3)/2

sova

2020-06-10 12:03:29

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sin^4x-cos^4x=(sin^2x-cos^2x)*(sin^2x+cos^2x)=-cos2x

-cos2x ≤ √3/2 ⇒ cos2x ≥ -√3/2 ⇒ (-π/6)+2πn ≤2 x ≤ (π/6)+2πn, n ∈ Z

[b](-π/12)+πn ≤ x ≤ (π/12)+πn, n ∈ Z[/b]