Sinx+cosx=-1 решите уравнение

Question

Sinx+cosx=-1 решите уравнение

Answer 1

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