A factor of cos(declination) in the formula of apparent of drift velocity of stars The angular drift velocity of stars is not the same for all stars and goes as $\frac{1}{\cos(\delta)}$. I don't understand why it should depend on the declination. All stars have to cover an angle of 360° in one sidereal day. Why should the angular velocity depend on the declination at all?
All stars have to cover an angle of 360° in one sidereal day.

is close but incomplete; we should really say that right ascension covers 360° in one sidereal day.
Let me state that analogy: Imagine that you are near the north pole. You start walking with the velocity of 5 km/h to the east. In a short amount of time, you are at the beginning. You went through all the time zones and geographical longitudes. Now you fly to the equator and do the same. Now you need a lot of time to go around the Earth. Change of geographical longitude is same in both cases. But the angle, measured from the center of the Earth, is different - at the north pole 0° and at the equator 360°.
With that analogy, you can understand the stars movement.
Let me give the last proof: has the north pole star same angular speed as Rigel?