I see that in mathematics text, “Prove that” is translated to German as “Man beweise, dass”, and “Determine” is translated as “Man bestimme”. What kind of construction is this? It reminds me of the imperative, but this is not quite the same. For imperative it would be “Beweise, dass …” (du form) or “Beweisen Sie, dass …” (Sie form).
This construction uses a form of subjunctive (Konjunktiv I) in the main clause and expresses a request, more or less equivalent in meaning to a sentence using the imperative. The imperative form is actually used in some mathematical texts as well, particularly more recent texts.
The imperative can be perceived as quite blunt; on the other hand, man + subjunctive is obsolescent, but has the advantage that no decision about du or Sie is required.
Formerly, the man + subjunctive construction was commonly used in recipes and similar instructional texts. A well-known advertising slogan for a company producing baking powder, instant pudding etc. is derived from this: Man nehme Dr. Oetker.