Question

Найти число корней из отрезка [-4П; 2П] ctg ( 2x-П/6)=1

Answer 1

ctg (2x-π/6)=1;

2x-π/6=π/4+πk;

2x=3π/12+2π/12+πk;

x=5π/24+kπ/2;

Найдем кол-во корней:

$-3\frac{19\pi}{24};\ -3\frac{7\pi}{24};\ -2\frac{19\pi}{24};\ -2\frac{7\pi}{24};\ -1\frac{19\pi}{24};\ -1\frac{7\pi}{24};\ -\frac{19\pi}{24};\ -\frac{7\pi}{24};\\\frac{5\pi}{24};\ \frac{17\pi}{24};\ 1\frac{5\pi}{24};\ 1\frac{17\pi}{24};$

12 корней