sin (x+pi/4)= sin^3 x + cos^3 x

(sinx+cosx)(sin²x-sinxcosx+cos²x)-(sinxcosπ/4+sinπ/4cosx)=0(sinx+cosx)(1-1/2sin2x)-√2/2(sinx+cosx)=0(sinx+cosx)(1-1/2sin2x-√2/2)=0sinx+cosx=0/cosxtgx+1=0tgx=-1x=-π/4+πn,n∈z1/2sin2x=(2-√2)/2sin2x=2-√22x=(-1)^n*arcsin(2-√2)+πk,k∈zx=(-1)^n*1/2*arcsin(2-√2)+πk/2,k∈z