お互い (“otagai”) is a Japanese word which is a little tricky to translate into English directly, but roughly means something along the lines of “each other’s”, “one other’s” or “mutual”. A common expression which uses this phrase is the following:
- Let’s each try our best
Notice that this is a little different than “一緒に (issho ni) 頑張りましょう” which has the connotation of working or trying together whereas お互い can mean trying separately in our own ways.
お互い is also commonly used in the following form:
- お互い + pre-masu form of verb + 合う (au)
The “pre-masu + 合う” part means to do a verb together and the お互い emphasizes this condition.
- お互い助け合う家族がいいね (助ける, tasukeru => to help)
- (I feel that) A family that helps one another is really nice.
Another way you see お互い used is in the expression “お互い様” (otagaisama) which is used to express two people are in the same position or situation.
- Person A: 意地悪！ (ijiwaru)
- Person A: (you’re) mean!
- Person B: お互い様だろう
- Person B: That makes two of us!
While the “sama” word here is spelled with the same Kanji as in the polite “sama” (like in 王様, ousama), I believe here さま instead carries the meaning of “state” or “condition” (said in Japanese as ありさま or 様子). Other similar phrases with a similar usage of さま are お疲れさま, ご苦労さま, and ごちそうさま.
As a final note, the first expression I mentioned (お互い頑張りましょう）would be appropriate for a superior to say to someone in his or her team, but the reverse (saying it to someone of a higher social ‘level’) is considered rude by some since it has the connotation that both people are on the same level. See this post for details on that (in Japanese).
What is the difference with お互いに?
I believe this has the same basic meaning, though in my experience the に is used less often. In certain situations particles can be safely omitted from Japanese and I think this applies here.
I think some cases where you are doing an action ‘towards’ both parties it might be slightly more natural to use the に, as in 「お互いに送りあう」.
My understanding is that “otagai-sama” as an exclamation means something like “pot calling the teakettle black”, as in the English, “You are!”
Yes, I agree, though I very rarely hear/use that expression in real conversation. I think “Look whose talking!” is a little more common, though still a bit cheesy…