Question

задание во вложении.

Answer 1

1 + 3Cos2x + Sin2x = 0
Sin²x + Cos²x  + 3(Cos²x - Sin²x) + 2SinxCosx = 0
Sin²x + Cos²x + 3Cos²x - 3Sin²x + 2SinxCosx = 0
- 2Sin²x + 2SinxCosx + 4Cos²x = 0
Sin²x - SinxCosx - 2Cos²x = 0
Разделим почленно на Сos²x , Cosx ≠ 0
tg²x - tgx - 2 = 0
Сделаем замену tgx = m
m² - m - 2 = 0
D = (- 1)² - 4 * 1 * (- 2) = 1 + 8 = 9 = 3²
$m_{1}= \frac{1+3}{2} =2\\\\ m_{2}= \frac{1-3}{2}=-1\\\\tgx = 2\\\\x _{1} =arctg2 + \pi n\\\\tgx= - 1\\\\ x_{2}=arctg(-1)+ \pi n\\\\ x_{2}=- \frac{ \pi }{4}+ \pi n \\\\\\tg( x_{o})= tg \frac{3 \pi }{4} =-1$