Question

cos2x=sinx-cosx тригонометрическое уравнение

Answer 1

cos²x-sin²x-(sinx-cosx)=0
(cosx-sinx)(cosx+sinx)+(cosx-sinx)=0
(cosx-sinx)(cosx+sinx+1)=0
cosx-sinx=0/cosx
1-tgx=0
tgx=1
x=π/4+πn,n∈z
cosx+sinx+1=0
2cos²(x/2)+2sin(x/2)cos(x/2)=0
2cos(x/2)*(cos(x/2)+sin(x/2)=0
cos(x/2)=0
x/2=π/2+πk
x=π+2πk,k∈z
cos(x/2)+sin(x/2)=0/cos(x/2)
1+tg(x/2)=0
tg(x/2)=-1
x/2=-π/4+πm
x=-π/2+2πm,m∈z