Question

помогите пожалуйста
полное решение ​

Answer 1

Ответ:

${ \tan {}^{2} (x) } - 5 = 4 \tan(x) \\ \tan(x) = y \\ {y}^{2} - 5 = 4y \\ {y}^{2} - 4y - 5 = 0 \\ y1y2 = - 5 \\ y1 + y2 = 4 \\ \\ y1 = 5 \\ y2 = - 1 \\ \\ \tan1(x) = 5 \\ \tan2(x) = - 1 \\ \\ x1 = arctan(5) \\ \\ x = arctan(5) + k\pi \: \\ \\ x2 = \frac{3\pi}{4}$