plot of $\sin(x) + \sin(y)= \cos(x) + \cos(y)$ I was playing arround with implicit plots of the form $f(x,y) = g(x,y)$, and I noticed that if you plot in the plane the following equation: $\sin(x) + \sin(y)= \cos(x) + \cos(y)$ you get the following graph:

My question is why does this trigonometric functions give us this squares spanning the entire plane?

Using Prosthaphaeresis Formulas
$$2\sin\dfrac{x+y}2\cos\dfrac{x-y}2=\cos\dfrac{x+y}2\cos\dfrac{x-y}2$$
If $\cos\dfrac{x-y}2=0\implies\dfrac{x-y}2=(2n+1)\dfrac\pi2, x-y=(2n+1)\pi$
else $\sin\dfrac{x+y}2=\cos\dfrac{x+y}2\iff\tan\dfrac{x+y}2=1\implies\dfrac{x+y}2=m\pi+\dfrac\pi4\iff x+y=\dfrac{(4m+1)\pi}2$
So we are getting continuous perpendicular & equidistant straight lines.
In the first case, the distance between two consecutive lines is $$\dfrac{2(m+1)+1-(2m+1)}{\sqrt2}\cdot\pi$$
and in the second, $$\dfrac{2\pi}{\sqrt2}$$
So,  we get infinite number of squares with each side $=\sqrt2\pi$
