Sin(px)+cos(px)=[latex] \sqrt{2} [/latex]

[latex]sin(\pi x)+cos(\pi x)=\sqrt{2}[/latex] [latex]\frac{1}{\sqrt{2}}*sin(\pi*x)+\frac{1}{\sqrt{2}}*cos(\pi*x)=1[/latex] [latex]sin(\pi*x)*cos \frac{\pi}{4}+sin \frac{\pi}{4}cos(\pi*x)=1[/latex] [latex]sin(\pi*x+\frac{\pi}{4})=1[/latex] [latex]\pi*x+\frac{\pi}{4}=\frac{\pi}{2}+2*\pi*k[/latex] [latex]x=\frac{1}{4}+2*k[/latex] k є Z