{ cosx*cosy =3/4 ; x - y =π/3 .
{ (cos(x+y) +cos(x-y))/2 =3/4 ; x - y =π/3 .
{(cos(x+y) +cos(π/3) =3/2 ; x - y =π/3 .
{cos(x+y) +1/2 =3/2 ; x - y =π/3 .
{cos(x+y) =1 ; x - y =π/3 .
{x+y =2πn ; x - y =π/3 , n∈Z .(сложим и вычитаем уравнения системы)
{x=π/6+πn ,y= πn -π/6 , n∈Z .
ответ: x=π/6+πn ,y= πn -π/6 , n∈Z .