Решите систему : x + y = Пи/2 cosx + siny = -1

Question

Решите систему :
x + y = Пи/2
cosx + siny = -1

Answer 1

X+y=π/2⇒y=π/2-x
cosx+siny=-1
cosx+sin(π/2-x)=-1
cosx+cosx=-1
2cosx=-1
cosx=-1/2
x=-2π/3⇒y=π/2+2π/3=7π/6
x=2π/3⇒y=π/2-2π/3=4π/3