1+sinx+cosx+sin2x+cos2x=0
1+sinx+cosx+2sinx*cosx+2cos²x-1=0
sinx+cosx+2sinx*cosx+2cos²x=0
sinx+cosx+2cosx(sinx+cosx) =0
(sinx+cosx) (1+2cosx) =0
sinx+cosx=0|:cosx
tgx+1=0
tgx=-1
x=-π/4+πn, n € Z
1+2cosx=0
cosx=-1/2
x=±2π/3+2πn, n € Z
Ответ: -π/4+πn; ±2π/3+2πn.