Решите уравнение 5sin2x-4sinxcosx+3cos2x=0

5sin2x - 4sinxcosx + 3cos2x=0
5sin2x - 2sin2x + 3cos2x = 0
3sin2x + 3cos2x = 0 делим на 3
cos^2(x) + 2sinxcosx - sin^2(x) = 0 делим на cos^2(x)
1 + 2tgx - tg^2(x) = 0
tg^2(x) - 2tgx - 1 = 0 назначим tg(x) = t
t^2 - 2t - 1 = 0 решим
D = 4 + 4 = 8
t1 = (2 + 2* $\sqrt{2}$ ) / 2 = 1 + $\sqrt{2}$
t2 = (2 - 2* $\sqrt{2}$ ) / 2 = 1 - $\sqrt{2}$

tgx = 1 + $\sqrt{2}$
x = arctg(1 + $\sqrt{2}$ ) + $\pi$ *n где n ∈ Z

tgx = 1 - $\sqrt{2}$
x = arctg(1 - $\sqrt{2}$ ) + $\pi$ *n где n ∈ Z