Задача 78049 ...

6643531e7295381996cf2b8d

5/14/2024 12:05:36 PM

{X+y= π }{-tgxtgy=1/3}

5f3eaa23faf909182968dde0

8/9/2024 7:10:18 PM

★

{x+y=π,
{-tgxtgy=1/3;

{y=π-x,
{-tgx*tg(π-x)=1/3;

{y=π-x,
{-tgx*(-tgx)=1/3;

{y=π-x,
{tg^(2) x=1/3;

{y=π-x,
{tgx= ± (sqrt(3))/3;

1) tgx=-(sqrt(3))/3,
x=arctg(-(sqrt(3))/3)+πk, k ∈ Z,
x_(1)=-(π/6)+πk, k ∈ Z,
y_(1)=π+(π/6)-πk=(7π)/6-πk, k ∈ Z;

2) tgx=(sqrt(3))/3,
x=arctg((sqrt(3))/3)+πn, n ∈ Z,
x_(2)=(π/6)+πn, n ∈ Z,
y_(2)=π-(π/6)-πn=(5π)/6-πn, n ∈ Z.

Ответ: (-(π/6)+πk;(7π)/6-πk), k ∈ Z;
((π/6)+πn; (5π)/6-πn), n ∈ Z.