Решить уравнение: sinx+sin5x=2cos2x
Sin x + sin 5x = 2cos 2x 2 sin 3x cos 2x = 2cos 2x 2 sin 3x cos 2x - 2cos 2x = 0 cos2x (sin3x - 1) = 0 cos2x = 0 | sin 3x -1 = 0 x = π/4 + πk/2, k∈Z | sin 3x = 1 | 3x = π/2 + 2πk | x = π/6 + 2/3πk, k ∈ Z Ответ: x = π/4 + πk/2, x = π/6 + 2/3πk, k∈Z