Hi I'm from Taiwan and I'm a native Chinese speaker. In my opinion toward the question, Either one works. Those two are all about 'May I take a look?' There's no one more formal than the other cause it Depends on How you Say that sentence :) (I mean they're all formal and they mean the same thing. ) Umm as for 看看 and 看一下 it just depends on the way you talk like sometimes we say "What's up?" yet sometimes we say "sup?" However they all refereed to the same thing :) Actually I say both of those too. Maybe at this moment I wanna say 我可以看看嗎? And the other point I wanna say 我可以看一下嗎? I hope my answer could help a little bit ^___^

I think both of them are ok.

They are both appropriate to use in a professional setting. They are also common in casual conversation. No difference. However, 看看 can be used when you are very angry with someone who has done something badly, in which case you cannot use 看一下. e.g. 你看看, 你把家里搞成什么样了! you can say it to someone when they have made a mess at home.

Duplication of a verb and the "（Verb）+一下“ pattern have exactly the same meaning and effect.

可以看看吗？ 可以看一下吗？