Question

Найдите сумму корней уравнения
$tan( frac{x}{2 } ) = - 1$
принадлежащих промежутку
$( - frac{3pi}{5} frac{18pi}{5} )$
1)
$2pi$
2)
$3.5pi$
3)
$4.5pi$
4)другой ответ​

Answer 1

1)tg x = -1

x/2 = -π/4 + πk

x = -π/2 + 2πk

2)-3π/5 < -π/2 + 2πk < 18π/5 |+π/2

-π/10 < 2πk < 41π/10|:2π

-1/20 < k < 41/20

-1/20 < k < 2 1/20

k = 0; 1; 2

3)x = -π/4

x = π-π/4 = 3π/4

x = 2π-π/4 = 7π/4

Ответ: {-π/4; 3π/4; 7π/4}