1+4 * sinx * cosx + 2cos^2x=0

sin^2x+ cos^2x + 4*sinx*cosx + 2 cos^2x=0

sin^2x +4*sinx*cosx + 3cos^2x=0 |:cos^2x

tg^2x + 4tgx +3 = 0

tgx = t

t^2 +4T+3=0

t1=0

t2=-4

x=Пk ; kЭ Z

x= arctg4 +Пk ; KЭZ