Question

решите уравнение sinx-cosx=1

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