Задача 76074 ...

632f635587d19127bff140f0

3/1/2024 5:54:43 PM

Решите уравнение: сos 4x + cos 2x = 0. Ответы: π/3+πn/3, n ∈ Z, π/2+πk, k ∈ Z. (–1)n π/9+πn/3, n ∈ Z, π/2+πk, k ∈ Z. π/6+πn/3, n ∈ Z, π/2+πk, k ∈ Z. π/6+πn, n ∈ Z, π/2+ πk, k ∈ Z.

626fab9a354ab65fb2f43abb

3/1/2024 6:27:55 PM

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cos 4x + cos 2x = 0
[m]2cos \frac{4x+2x}{2} cos \frac{4x-2x}{2} = 0[/m]
2cos 3x*cos x = 0
1)cos x = 0
[b]x1 = π/2 + π*k, k ∈ Z[/b]
2) cos 3x = 0
3x = π/2 + π*n, n ∈ Z
[b]x2 = π/6 + π/3*n, n ∈ Z[/b]