Tan(x)+tan(y)=22*cos(x)*cos(y)=1решить систему уравнений

{2cosxcosy=1⇒cosxcosy=1/2 {tgx+tgy=2 sinx/cosx+siny/cosy=2 (sinxcosy+sinycosx)/coscosy=2 sin(x+y)/cosxcosy=1/2 sin(x+y)=2coscosy sin(x+y)=2*1/2 sin(x+y)=1 x+y=π/2 y=π/2-x tgx+tg(π/2-x)=2 tgx+ctgx=2 tgx+1/tgx-2=0 tg²x+1-2tgx=0 (tgx-1)²=0 tgx-1=0 tgx=1 x=π/4 y=π/2-π/4 y=π/4 Ответ x=π/4+πn,n∈z;y=π/4+πn,n∈z