Tg(x+π/4)+tg(x-π/4)=tgx
(tgx+tgπ/4)/(1-tgx*tgπ/4)+
(tgx-tgπ/4)/(1+tgx*tgπ/4)=tgx
(tgx+1)/(1-tgx)+(tgx-1)/(1+tgx)=tgx
(1+2tgx+tg^2x-tg^2x+2tgx-1)/(1-tg^2x)=tgx
4tgx/(1-tg^2x)-tgx=0
tgx=0;1-tg^2x#0
x=π/4+πk;k€Z
4/(1-tg^2x)-1=0
(4-1+tg^2x)/(1-tg^2x)=0
3+tg^2x=0
tg^2x=-3
нет решения
ответ π/4+πk;k€Z