Question

4sin^2x+sin2x=3 помогите пожалуйста

Answer 1

$4sin^2x + sin2x = 3 \\ 4sin^2x - 3 + 2sinxcosx = 0 \\ 3sin^2x - 3 + sin^2x + 2sinxcosx = 0 \\ sin^2x + 2sinxcosx - 3cos^2x = 0 \\ tg^2x + 2tgx- 3 = 0$
Пусть $t = tgx.$
$t^2 + 2t - 3 = 0 \\ \\ t_1 + t_2 = -2 \\ t_1 \cdot t_2 = -3 \\ \\ t_1 = -3 \\ t_2 = 1$
Обратная замена:
$tgx = -3 \\ \boxed{x = arctg(-3) + \pi \pi n, \ n \in Z} \\ tgx = 1 \\ \boxed{x = \frac{ \pi}{4} + \pi n, \ n \in Z. }$