Question

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

Answer 1

(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)=0
sinx+cosx=0/cosx
tgx+1=0
tgx=-1
x=-π/4+πn,n∈z
1/2sin2x=(2-√2)/2
sin2x=2-√2
2x=(-1)^n*arcsin(2-√2)+πk,k∈z
x=(-1)^n*1/2*arcsin(2-√2)+πk/2,k∈z