решить систему tgx*tgy=1, sinx*cosy+ctgx*tgy=1/2

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