The ostensible potential of renewable alternatives to ecologically deleterious hydrocarbons may, paradoxically, (i) _______ the fossil-fuel sector by reconceptualizing energy crises not as a function of profligate consumption, but as a rectifiable deficiency in green production; this shift in discourse inveigles the populace to (ii) _______ the very paradigms of expenditure from which these industries continue to derive their windfall.

When we have a TC with such complex clauses like this one, the best thing to do would be to simplify and rewrite it on your scratch paper.

Below we have a stripped down version:

Renewable energy which is an alternative to harmful fossil-fuels may paradoxically (i) _______ the fossil-fuel sector by redefining energy crises as rectifiable; this shift in thinking convinces the population to (ii)_________ the type of expenditure from which the fossil-fuel sector derive its profits.

We have the word "paradoxically" which indicates a contrast shift. Therefore, renewable energy which can replace fossil-fuels can paradoxically only end up supporting the fossil-fuel sector. The word is buttress. And this shift in thinking can only convince the population to agree to the type of expenditure from which this fossil-fuel sector derives its profits. The word is acquiesce in. And this last sentence fragment continues the idea of paradoxically benefitting the fossil-fuel sector, as it should, thanks to the semi-colon.

The word inveigles means to persuade, lure, or entice someone through deception, flattery, or artful maneuvering. This itself suggests the word for the second blank should be acquiesce in. Once you get this right, the first blank should have a word that ensures that the fragment before the semi-colon, agrees with the meaning of the sentence fragment containing the second blank. The reason for this is the semi-colon(;) after "rectifiable" indicates that the same meaning or sentiment continues, and there is no change in direction of meaning or sentiment. And the only way to accomplish this through the word buttress.

The choices are buttress and acquiesce in.