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 - siny + 1/2 = 0

siny = t
1/2t - t + 1/2 = 0
t - 1/2t - 1/2 = 0
2t - t - 1 = 0
t = 1
t = -1/2

siny = 1
siny = -1/2


sinx = 1/2 - siny
siny = 1

sinx = -1/2
siny = 1

x = -/6 + 2n
x = -5/6 + 2n
y = /2 + 2n

sinx = 1/2 - siny
siny = -1/2

sinx = 1
siny = -1/2

x = /2 + 2n
y = -/6 + 2n
y = -5/6 + 2n

Ответ: (/2 + 2n; -/6 + 2n); (/2 + 2n; -5/6 + 2n); (-/6 + 2n; /2 + 2n); (-5/6 + 2n; /2 + 2n); nZ