Решить уравнение sin x + cos x = 1

возведем обе части в квадрат(sinx+cosx)²=1sin²x+2sinxcosx+cos²x=11+sin2x=1sin2x=02x=πk, k∈Zx=πk/2, k∈Z

2sin(x/2)cos(x/2)+cos²(x/2)-sin²(x/2)-sin²(x/2)-cos²(x/2)=02sin(x/2)cos(x/2)-2sin²(x/2)=02sin(x/2)*(cos(x/2)-sin(x/2))=0sin(x/2)=0⇒x/2=πn⇒x=2πn,n∈zcos(x/2)-sin(x/2)=0/cos(x/2)1-tg(x/2)=0tg(x/2)=1⇒x/2=π/4+πk⇒x=π/2+2πk,k∈z