Is 你怎么知道怎么做中国菜? (How do you know how to cook Chinese food?) a grammatically correct question? This is from a problem from my Chinese book; I'm practicing the use of 怎么 (zěn me).


  美国朋友会做中国菜，你觉得很奇怪，问他：...
  Měiguó péngyǒu huì zuò zhōngguó cài, nǐ juédé hěn qíguài, wèn tā: ...


This translates to "An American friend can cook Chinese food; you feel it's strange.  [You] ask him: ... "  I came up with two answers:



The first I think is fine: 你怎么会做中国菜？ (Nǐ zěnme huì zuò zhōngguó cài?) meaning "How can you cook Chinese food?"

My second answer I'm uncertain about because of the repeated 怎么, and because it's an almost-direct translation from English:


  你怎么知道怎么做中国菜？
  Nǐ zěnme zhīdào zěnme zuò zhōngguó cài?


By this I intend to ask him "How do you know how to cook Chinese food?"

Question: Is 你怎么知道怎么做中国菜? a grammatically correct question?
你怎么知道如何做中国菜？

or without how

你在哪学会做中国菜？