Question

sin(px)+cos(px)=$sqrt{2}$

Answer 1

$sin(pi x)+cos(pi x)=sqrt{2}$
$frac{1}{sqrt{2}}*sin(pi*x)+frac{1}{sqrt{2}}*cos(pi*x)=1$
$sin(pi*x)*cos frac{pi}{4}+sin frac{pi}{4}cos(pi*x)=1$
$sin(pi*x+frac{pi}{4})=1$
$pi*x+frac{pi}{4}=frac{pi}{2}+2*pi*k$
$x=frac{1}{4}+2*k$
k є Z