Решим систему уравнений:

1) 2sin(x/2) = √2
sin(x/2) = √2 / 2 = √2 / √2 = 1
Так как sin(90 градусов) = 1, получаем x/2 = 90 градусов = π/2
x = 2π

2) 2cos(x) = 3√2
cos(x) = 3√2 / 2 = 3 / 2
Так как cos(30 градусов) = √3 / 2, получаем x = π/6

3) 2cos(2x+π/4) = 0
cos(2x + π/4) = 0
2x + π/4 = π/2
2x = π/2 - π/4 = π/4
x = π/8

4) sin(x + 3π/4) = 0
x + 3π/4 = 0
x = -3π/4

Итак, решения системы уравнений:
x = 2π, x = π/6, x = π/8, x = -3π/4.