The general solution of the trigonometrical equation sin⁡x+cos⁡x=1 is

sin⁡x+cos⁡x=1⇒sin⁡(x+π/4)=12=sin⁡π4⇒ x+π4=nπ+(−1)nπ4⇒ x=nπ+(−1)nπ4−π4which includes x=2nπ and x=2nπ+π2.