Решить уравнение sin x+sin 5x=0
Решение sin x+sin 5x=0 2sin(x + 5x)/2 * cos((x - 5x)/2 = 0 sin3x * cos(-2x) = 0 1) sin3x = 0 3x = πk, k ∈Z x₁ = πk/3, k ∈ Z 2) cos2x = 0 2x = π/2 + πn, n ∈Z x₂ = π/4 + πn/2, n ∈Z Ответ: x₁ = πk/3, k ∈ Z; x₂ = π/4 + πn/2, n ∈Z