Question

Решите уравнение прошу

Answer 1

3tg²x + 2tgx - 1 = 0
Сделаем замену   tgx = m
3m² + 2m - 1 = 0
D = 2² - 4 * 3 * (- 1) = 4 + 12 = 16 = 4²
$m_{1}= frac{-2+4}{6} = frac{1}{3} \\ m_{2} = frac{-2-4}{6}=-1\\tgx= frac{1}{3} \\x=arctg frac{1}{3}+ pi n \\\tgx=-1\\x=arctg(-1)+ pi n\\x=- frac{ pi }{4} + pi n,n$∈z