Задача 52332 ...

vk193930936

2020-06-10 17:06:14

sin(π/3-2x)*cos(π/3-2x) ≥ -sqrt(3)/4

sova

2020-06-10 17:21:29

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Формула
sin α *cos α =(1/2)sin2α

(1/2)sin((2π/3)-4x) ≥ -√3/4 ⇒ sin((2π/3)-4x) ≥ -√3/2

sin(4x-(2π/3) ≤ √3/2

(-4π/3) +2πn ≤ 4x-(2π/3) ≤ (π/3)+2πn, n ∈ Z

(-4π/3) +(2π/3)+2πn ≤ 4x ≤ (π/3)+(2π/3)+2πn, n ∈ Z

(-2π/3)+2πn ≤ 4x ≤ π+2πn, n ∈ Z

[b](-π/6)+(π/2)n ≤ x ≤ (π/4)+(π/2)n, n ∈ Z[/b]