Cos2x+5sinx*cosx+5cos^2x=0 , , буду

 cos2x + 5sinx·cosx + 5cos²x = 0
cos²x - sin²x + 5sinx·cosx + 5cos²x = 0
6cos²x - sin²x + 5sinx·cosx  = 0    делим на cos²x
6 - tg²x + 5tgx = 0
tgx = t
t² - 5t - 6 = 0
D = 25 + 24 = 49
t = 6    или    t = - 1
tgx = 6                  tgx = -1
x = arctg6 + πn    x = -π/4 + πk