Решить уравнение 2sin(4x+π/2)+√2=0

Question

Решить уравнение
2sin(4x+π/2)+√2=0

Answer 1

Sin(4x+π/2)=-√2/2
4x+π/2=(-1)^k * arcsin(-√2/2) + πk, k∈Z
4x+π/2=(-1)^(k+1) * π/4 + πk, k∈Z
4x=(-1)^(k+1) * π/4 -π/2+ πk, k∈Z
х=(-1)^(k+1) * π -2π + 4πk, k∈Z.