1. I applied cosmetics on my face.

2. I applied the cosmetics on my face.
3. I applied makeup on my face.
4. I applied the make-up on my face.
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Which expressions are correct?

All seem to be correct, except that I don't think the hyphen is needed in #4.

=)

Thank you. By the way. in which case do we use 'the'?

Most of the time "the" is used to indicate something rather specific. It's idiomatic, though, and not always easy to explain or understand.

Here's a webpage where articles (a, an, the) are discussed:
http://grammar.ccc.commnet.edu/grammar/determiners/determiners.htm

=)

All of the expressions you mentioned are grammatically correct. However, there are slight differences in meaning and usage.

1. "I applied cosmetics on my face." - This sentence is correct and can be used to talk about applying multiple cosmetic products on your face. It is a general statement and does not specify which specific cosmetics were applied.

2. "I applied the cosmetics on my face." - This sentence is also correct, but it implies that you are referring to specific cosmetics that were mentioned or implied previously in the conversation. The use of "the" suggests a specific set of cosmetics.

3. "I applied makeup on my face." - This sentence is correct and commonly used to describe putting on cosmetics, specifically for the face. "Makeup" is a more general term that encompasses a range of cosmetics such as foundation, blush, mascara, etc.

4. "I applied the make-up on my face." - Similar to the second sentence, this sentence implies a specific set of makeup that was mentioned or implied before. The use of "the" indicates a specific makeup product.

In conclusion, all four sentences are grammatically correct, but the choice of expression depends on the specific context and the level of specificity you want to convey.