Final answer:
The sentence that indicates the cyclic process of birth and death of stars is: 'Any interstellar grains that are incorporated into newly forming stars will be destroyed by their high temperatures. But eventually, each new generation of stars will evolve to become red giants, with stellar winds of their own. Some of these stars will also become supernovae and explode. Thus, the process of recycling cosmic material can start all over again.'
Step-by-step explanation:
The sentence from the article that helps the reader infer that birth and death of stars is a cyclic process is: Any interstellar grains that are incorporated into newly forming stars (instead of the colder planets and smaller bodies around them) will be destroyed by their high temperatures. But eventually, each new generation of stars will evolve to become red giants, with stellar winds of their own. Some of these stars will also become supernovae and explode. Thus, the process of recycling cosmic material can start all over again. This sentence illustrates that from the remains of dying stars, new generations of stars are formed, going through different stages and eventually exploding or becoming red giants, which indicates a cyclic process of birth and death of stars.