Cos2x+sin2x+2sin²x+sinx+cosx=0
cos²x-sin²x+2sinxcosx+2sin²x+sinx+cosx=0
sin²x+2sinxcosx+cos²x+sinx+cosx=0
(sinx+cosx)²+(sinx+cosx)=0
(sinx+cosx)(sinx+cosx+1)=0
1) sinx+cosx=0
√2sin(x+π/4)=0
sin(x+π/4)=0
x+π/4=πn
x=-π/4+πn,n∈Z
2) sinx+cosx+1=0
sinx+cosx=-1
√2sin(x+π/4)=-1
sin(x+π/4)=-√2/2
x+π/4=(-1)ᵏ•(-π/4)+πk
x=(-1)ᵏ⁺¹•(π/4)-π/4+πk,k∈Z.