Он должен справиться с этой проблемой самостоятельно.

Questions & Answers about Он должен справиться с этой проблемой самостоятельно.

Could we use один instead of самостоятельно here?
Yes! You could say Он должен справиться с этой проблемой один. However, they have slightly different flavors. один simply means "alone" (nobody else is there), while самостоятельно means "independently" or "by oneself" (without relying on others' help). When talking about handling a problem, both work perfectly.
Why is эта проблема in the instrumental case here (этой проблемой)?
The verb справиться (to handle / cope) always pairs with the preposition с (with). In Russian, "with" usually requires the instrumental case. Therefore, the feminine phrase эта проблема changes to этой проблемой.
Why use the perfective verb справиться instead of the imperfective справляться?
We use the perfective aspect because the focus is on successfully completing a single action. He is expected to solve this specific problem completely, rather than just coping with problems on a regular, ongoing basis.
Is должен a verb?
должен is actually a "short-form adjective" that is used to express obligation (must / have to). Because it's an adjective, it changes to match the gender and number of the subject. Here it is masculine to match Он, but if the subject were a woman, it would be Она должна, and for plural subjects, Они должны.

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