Question

ПОМОГИТЕ!!!Решить систему:
x-y=П/2
Sinx+siny = - корень из 2

Answer 1

1) x-y=π/2, 
2) sinx+siny =-√2;
1) x=π/2+y;
2) sin(π/2+y)+siny=-√2;
2sin(π/4+y)cosπ/4=-√2;
sin(π/4+y)*√2/2=-√2/2;
sin(π/4+y)=-1;
π/4+y=-π/2+2πn, n∈Z;
y=-π/2-π/4+2πn, n∈Z;
y=-3π/4+2πn, n∈Z.
1) x=π/2-3π/4+2πn, n∈Z;
x=-π/4+2πn, n∈Z.
Ответ: (-π/4+2πn, n∈Z; -3π/4+2πn, n∈Z)