Задача 46623 ...

vsegodobrogo

2020-04-10 11:50:27

2cos²x + sqrt(2)cosx = 0.

sova

2020-04-10 11:55:00

★

cosx*(2cosx+sqrt(2))=0
cosx=0 или 2cosx+sqrt(2)=0

cosx=0 ⇒ [b] x=(π/2)+πk, k ∈ Z[/b]

cosx=-sqrt(2)/2 ⇒ ± arccos(-sqrt(2)/2) +2πn, n ∈ Z

[b]x=±(3π/4)+2πn, n ∈ Z[/b]