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:

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

12 корней