1.
I'm sorry to trouble you; excuse me for bothering you
A humble expression used when making a request or causing inconvenience.
恐れ入りますが、もう一度説明していただけますか。
I'm sorry to trouble you, but could you explain that once more?
恐れ入りますが、少々お待ちください。
I'm sorry, but please wait a moment.
恐れ入りますが、こちらにご署名をお願いいたします。
I'm sorry to trouble you, but please sign here.
お忙しいところ恐れ入りますが、確認をお願いできますか。
I know you're busy, but could I ask you to check this?
2.
thank you very much; I'm much obliged
A humble expression of gratitude when someone has done something for you.
わざわざお越しいただき、恐れ入ります。
Thank you so much for taking the trouble to come.
ご配慮いただき、恐れ入ります。
I'm very grateful for your consideration.
FORMALITY:
This is a very polite/humble expression commonly used in business settings and customer service. The past form 恐れ入りました is also used.
COMMON PATTERNS:
- 恐れ入りますが〜 - I'm sorry to trouble you, but... (preceding a request)
- お忙しいところ恐れ入りますが - I know you're busy, but...
- わざわざ〜恐れ入ります - Thank you for going out of your way to...
RELATED EXPRESSIONS:
- 申し訳ございません - I'm terribly sorry (apologizing for trouble caused)
- 失礼いたします - Excuse me (more general)