Понижаем степень у косинуса по формуле
cos²(x) = (1 + cos(2x))/2
1. cos² 4x = 1/2
(1 + cos 8x) / 2 = 1/2
1 + cos 8x = 1
cos 8x = 0
8x = π(n + 1)/2, n∈Z
x = π(n + 1)/16, n∈Z
2. cos²(x / 4) = 1/4
(1 + cos (x/2))/2 = 1/4
1 + cos(x/2) = 1/2
cos(x/2) = -1/2
x/2 = ±2π/3 + 2πm, m∈Z
x = ±4π/3 + 4πm, m∈Z