Стригонометрией sin2x+sinx+cosx+1=0

(sinx+cosx)^2+(sinx+cosx)=0
(sinx+cosx)(sinx+cosx+1)=0
sinx=-cosx
tgx=-1
x=-П/4+Пk
sinx+cosx=-1
√2/2sinx+√2/2cosx=-√2/2
cos(x-П/4)=-√2/2
x-п/4=П-П/4+2Пk
x=П+2Пk=П(2k+1)
x=3П/2+2Пk=П/2(3+4k)