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:
$tgx = -3 \ boxed{x = arctg(-3) + pi pi n, n in Z} \ tgx = 1 \ boxed{x = frac{ pi}{4} + pi n, n in Z. }$