Задача 66618 cos 2х – cos х = cos 3х...

636159f51328ba2972ebb987

01.11.2022 20:42:19

cos 2х – cos х = cos 3х

5f3ea7e3faf909182968ddd9

01.11.2022 23:38:50

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cos2x=cos3x+cosx

cos2x=2cos2x*cosx

cos2x-2cos2x*cosx=0

cos2x*(1-2cosx)=0


cos2x=0 или 1-2cosx=0

2x=(π/2)+πn, n ∈ Z

[b]x=(π/4)+(π/2)*n, n ∈ Z[/b]

или

1-2cosx=0

сosx=1/2

x= ± arccos(1/2)+2πk, k ∈ Z

[b]x= ± (π/3)+2πk, k ∈ Z[/b]