1. I will be a musician one day.

2. I will be a musician some day.
(Which one is correct? Are both OK? Then which one is commonly used?)

3. She is putting on cosmetics on her face.
4. She is wearing cosmetics on her face.
5. She is puting on makeup on her face.
6. She is wearing makeup on her face.
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Thank you for your help. Which ones are grammatical?

1 and 2 are both common, and mean the same.

3-6 are all grammatically correct, but the only way I'd say it is

she is wearing makeup (all finished)
she is putting on makeup (in the process)

use of the word "cosmetics" in such a context seems stilted to me.

The face is implied, and awkward if stated explicitly.

Regarding the first question, both sentences are grammatically correct. However, there is a slight difference in meaning.

"I will be a musician one day" suggests a future time frame that is likely to happen, indicating that becoming a musician is a definite goal or aspiration you believe will be achieved eventually.

"I will be a musician some day" implies a less specific time frame for achieving your goal. It suggests that becoming a musician is something you hope for but are unsure exactly when it will happen.

In terms of common usage, "I will be a musician one day" is more commonly used since it conveys a stronger sense of determination.

Moving on to the second question, all of the sentences are grammatically correct, but there are some differences in meaning.

3. "She is putting on cosmetics on her face" - This sentence implies that she is in the process of applying cosmetics at the moment.

4. "She is wearing cosmetics on her face" - This sentence suggests that she currently has cosmetics on her face but does not specifically indicate if she is in the process of applying them or has already completed the application.

5. "She is putting on makeup on her face" - This sentence is similar to sentence 3 but uses the word "makeup" instead of "cosmetics." The meaning remains the same.

6. "She is wearing makeup on her face" - This sentence indicates that she currently has makeup on her face but does not imply any ongoing action of application.

All four sentences are grammatically correct, and the choice between them depends on the specific context and the intended meaning you wish to convey.