I like the fact that your answer does not depend on knowing that sine is an odd function. It appears that when using Euler to prove sine is odd one must make use of complex conjugates. Correct?
The meaning of PROVE is to establish the existence, truth, or validity of (as by evidence or logic). How to use prove in a sentence. proved or proven?: Usage Guide.
PROVE definition: 1. to show a particular result after a period of time: 2. to show that you are good at something…. Learn more.
To establish the truth or validity of (something) by the presentation of argument or evidence: The novel proves that the essayist can write in more than one genre. The storm proved him to be wrong in his prediction. b. To demonstrate the reality of (something): He proved his strength by doing 50 pushups. c.
prove (third-person singular simple present proves, present participle proving, simple past proved, past participle proved or proven) (transitive) To demonstrate that something is true or viable; to give proof for; to bear out; to testify.
PROVE definition: to establish the truth or genuineness of, as by evidence or argument. See examples of prove used in a sentence.
prove: To establish the truth or validity of (something) by the presentation of argument or evidence.
If something proves to be true or to have a particular quality, it becomes clear after a period of time that it is true or has that quality. None of the rumours has ever been proved to be true. [VERB to-infinitive] In the past this process of transition has often proven difficult. [VERB adjective]