Решить систему sin x+sin y=1/2, sin x*sin y=-1/2

Sinx + siny = 1/2

sinx * siny = - 1/2

sinx = 1/2 - siny

(1/2 - siny) * siny = - 1/2

sinx = 1/2 - siny

1/2siny - sin²y + 1/2 = 0

siny = t

1/2t - t² + 1/2 = 0

t² - 1/2t - 1/2 = 0

2t² - t - 1 = 0

t = 1

t = - 1/2

siny = 1

siny = - 1/2

sinx₁ = 1/2 - siny₁

siny₁ = 1

sinx₁ = - 1/2

siny₁ = 1

x₁ = - π/6 + 2πn

x₂ = - 5π/6 + 2πn

y₁ = π/2 + 2πn

sinx₃ = 1/2 - siny₂

siny₂ = - 1/2

sinx₃ = 1

siny₂ = - 1/2

x₃ = π/2 + 2πn

y₂ = - π/6 + 2πn

y₃ = - 5π/6 + 2πn

Ответ: (π/2 + 2πn; - π/6 + 2πn) ; (π/2 + 2πn; - 5π/6 + 2πn) ; (-π/6 + 2πn; π/2 + 2πn) ; (-5π/6 + 2πn; π/2 + 2πn) ; n∈Z