Задача 52342 ...

vk193930936

2020-06-10 18:35:49

2sin^(2)(2x)+2cos^(2)(x) ≥ 3

sova

2020-06-10 18:55:17

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2cos^2x=1+cos2x

sin^22x=1-cos^22x


2*(1-cos^22x)+1+cos2x-3 ≥ 0

2cos^22x-cos2x ≤ 0

cos2x*(2cos2x-1) ≤ 0 ⇒ 0 ≤ cos2x ≤ 1/2

(-π/2)+2πn ≤ 2x ≤(-π/3)+2πn или (π/3)+2πn ≤ 2x ≤(π/2)+2πn, n ∈ Z

[b](-π/4)+πn ≤ x ≤(-π/6)+πn или (π/6)+πn ≤ x ≤(π/4)+πn, n ∈ Z[/b]