Решите систему cosx + cosy = корень из 3 x + y = π/3

Question

Решите систему
cosx + cosy = корень из 3
x + y = π/3

Answer 1

X+y=π/3
x=π/3-y
cos(π/3-y)+cosy=√3
2cosπ/6*cos(π/6-y)=√3
2*√3/2*cos(π/6-y)=√3
cos(π/6-y)=1
sin(y+π/3)=1
y+π/3=π/2
y=π/2-π/3
y=π/6+2πn,n∈z
x=π/3-π/6
x=π/6+2πn,n∈z