Question

Tg(x+П/4)+tg(x-П/4)=2ctgx

Answer 1

tgx+1/1-tgx+tgx-1/1+tgx-2/tgx=0
tg²x+2tgx+1-tg²x+2tgx-1/1-tg²x-2/tgx=0
4tgx/1-tg²x-2/tgx=0
4tg²x-2+2tg²x/tgx(1-tg²x)=0
$\left \{ {{6tg^2x-2=0} \atop {tgx(1-tg^2x) \neq 0}} \right.$
tg²x=1/3
tgx=1/√3            tgx=-1/√3
x=π/6+πn            x=-π/6+πn
tgx≠0        tgx≠1          tgx≠-1
x≠πn        x≠π/4+πn    x≠-π/4+πn
ответ  +-π/6+πn