matematikk.net

Finn vinklene u,v e[0,pi] slik at
sin(x+u)+cos(x+v)=sqrt(2)*cosx

mattenøtta wrote:Finn vinklene u,v e[0,pi] slik at
sin(x+u)+cos(x+v)=sqrt(2)*cosx

[tex]\sin(x)\left(\cos(u)-\sin(v)\right)+\cos(x)\left(\sin(u)+\cos(v)\right)=\sqrt{2}\cos(x)[/tex]
DVs
[tex]\cos(u)-\sin(v)=0[/tex]
og
[tex]\cos(v)+\sin(u)=\sqrt{2}[/tex]
altså:
[tex]\cos(u)=\sin(v)[/tex]
og
[tex]\cos(u)=\frac{\sqrt{2}}{2}=\sin(v)[/tex]
der
[tex]u=v=\pi/4[/tex]