The verb 'nugu' 「脱ぐ」is used when referring to wearables like shirts, trousers or gloves, but not to things worn on the head, like hats. The verb to use when referring to taking off things worn on the head is 'toru' 「取る」. Therefore, the above sentence should be 'Take off your hat' 'booshi (w)o torinasai'「帽子を取りなさい」.
James Wiegert
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The dictionary says "帽子を脱ぐ" is the same as "帽子を取る".
https://www.weblio.jp/content/%...8F%96%E3%82%8B
We can see the verb "脱ぐ" with 帽子 on Google a lot.
I usually don't wear 帽子, so I can't say which is more popular.
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