Sinx - cosx = -sqrt2

sinx+sin(π/2+x)=-√2
2sin((2x+π/2)/2))*cos((x-x-π/2)/2)=-√2
sin(x+π/4)*cos(-π/4)=-√2/2
sin(x+π/4)*√2/2=-√2/2
sin(x+π/4)=-1
x+π/4π=3π/2+2π*n
x=5π/4+2π*n