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