Why the cos() factor?
If light falls on a surface, we wish to know how much falls on a particular area, say a square centimeter. That depends on the angle at which the light strikes the surface.
Let's say we cut a 1 cm ( 1 cm square hole in an opaque screen. If the sun is directly overhead (we say, at zenith), and we hold the screen parallel to a horizontal surface, a 1 cm ( 1 cm patch will be illuminated on the surface. Now let us move the sun to 30o solar zenith angle. Now we hold the screen perpendicular to the direction the light is traveling, and a larger patch is illuminated. But it is the same amount of light that passes through the hole, regardless of where sun is, as long as the plane of the hole is perpendicular to the direction the light is traveling. Thus, the amount of light that falls on a 1 cm2 portion of the illuminated surface is less than it was when the sun was at zenith.
If we make sure that one edge of the square hole is horizontal, then we can figure out how big the illuminated patch is. Need a figure for this discussion. The images of the top and bottom edges of the hole are the same size, regardless of the sun's zenith angle. But the length of the images of the other two edges is stretched out.