Final answer:
The true statement is that Beethoven wrote the Heiligenstadt Testament to his brothers, describing his despair over losing his hearing. His music evolved over time from a Classical to a Romantic style, and he did not die unknown and unappreciated.
Step-by-step explanation:
Option b is the true statement. Beethoven wrote a letter, known as the Heiligenstadt Testament, to his brothers Carl and Johann expressing the despair he felt at the knowledge that he was losing his hearing. This letter is well-documented in Beethoven's biographies and illustrates the personal challenges he faced with his deteriorating hearing.
On the other hand, the assertion in option a that Beethoven's music is written in essentially the same style throughout all periods of his life is incorrect. Beethoven's music evolved over time, with his early works being more Classical in style, and his later compositions becoming synonymous with the Romantic era, reflecting the trademark drama and human emotion.
The statement in option c that Beethoven died unknown and unappreciated is also false. Beethoven was recognized and celebrated as a composer during his lifetime, and his death was widely mourned.