Помогите решить уравнение 5sin^2x-25sinx*cosx+cos^2x=4

5sin^2x-25sinx*cosx+cos^2x=4

5sin^2x-25sinx*cosx+cos^2x=4 (sin^2x + cos^2x)

sin^2x - 25sinxcosx - 3cos^2x = 0 |:cos^2x

tg^2x - 25tgx - 3 = 0

tgx = t

t^2 - 25t - 3 = 0

D = 625 + 4*3 = 637

t = (25 + - 637^0,5) / 2

tgx = (25 + 637^0,5) / 2 tgx = (25 - 637^0,5) / 2

x = artctg[ (25 + 637^0,5) / 2] + Пk x = arctg (25 - 637^0,5) / 2 + Пk