Cos2x=sinx-cosx тригонометрическое уравнение

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