出演: a planned appearance and a declined invitation
Read 出演 in a friend's future stage appearance and a politely declined invitation. Distinguish what was arranged, what was requested and which action was completed.
出演することになった and an arranged appearance
出演 (しゅつえん) refers to appearing or performing. 「友人が町の演劇に出演することになった。」 means “My friend will appear in a local play.” The friend has an arranged future appearance in a local play; the English uses will appear.
出演することになった states that an appearance has been arranged. That arrangement and actually appearing in the play are different events, and this sentence gives no specific performance date.
出演依頼 as the request declined
「番組への出演依頼を丁寧に断った。」 means “I politely declined the invitation to appear on the program.” 番組への出演依頼 is an invitation to appear on the program. 丁寧に describes how the invitation was declined.
断った reports a completed refusal. The object refused is the request to appear, without reporting an appearance on the program or attendance as a spectator.
An arrangement and a completed refusal
The friend's future appearance is arranged in the first sentence, while declining an invitation is the completed action in the second. The shared word 出演 does not make these the same action.
Declining one invitation is a response to that request. It does not establish a permanent refusal of every future program; identify the particular request and the response made to it.
What was declined in 番組への出演依頼を丁寧に断った?
Show the answer and why
The invitation to appear on the program was politely declined. The completed action is the refusal, not an appearance. Keep that response distinct from the friend's arranged appearance in the play.