How can light be stretched (redshifted) if the speed of light is constant?

Question

If light travels at the same speed how can it be stretched to provide red shift that is used in measuring the expansion of the universe?

Answer 1

The statement "the speed of light is constant" refers to the local speed with which light passes through any given point in spacetime, according to an observer that is also passing through that point. The significance of this caveat for cosmology is explained here:

What does general relativity say about the relative velocities of objects that are far away from one another?

For the present question, the "local" caveat is important because successive wavecrests are spatially separated from each other: successive wavecrests cannot both pass through the same spacetime point. So there is no contradiction between "the speed of light is constant" and cosmological redshift. Whenever a given wavecrest passes through a given point in spacetime, its speed is the usual constant $c$ according to an observer who is also passing through that point. In contrast, the relative "speed" between two spatially-separated entities (such as successive wavecrests) is not fundamentally limited; it's not even obvious how such a speed should be defined. This is related to the possibility of a cosmological horizon.