Система неравенств{x+y=п/2 {корень из 3 +cos 2x =cos2y

Question

Система неравенств{x+y=п/2
{корень из 3 +cos 2x =cos2y

Answer 1

{x+y=п/2⇒x=π/2-y
{√3 +cos 2x =cos2y
√3+cos(π-2y)=cos2y
√3-cos2y=cos2y
2cos2y=√3
cos2y=√3/2
2y=π/6
y=π/12
x=π/2-π/12
x=5π/12
Ответ (5π/12+2πk;π/12+2πk,k∈z)