People
have discovered the principles of solar energy whenever fuel becomes scarce and expensive but will forget them every time a new source of cheap energy is developed.
from above we can figure out that we want to convey a fact so present tense is best way to convey this so A,B,C are out .
Note we need to express condition so whenever is correct usage .
(A) have discovered the principles of solar energy whenever fuel becomes scarce and expensive but will forget (doesn't make logical sense - the tenses don't match and mess up meaning )
(B) have discovered the principles of solar energy whenever fuel has become scarce and expensive but they forget
(C) discovered the principles of solar energy every time fuel becomes scarce and expensive, forgetting
(D) discover the principles of solar energy every time(THIS EVERYTIME DOESN'T FIT HERE AS WE ARE EXPRESSING A CONDITION) fuel
became (BECOMES) scarce and expensive, but they forget
(E) discover the principles of solar energy whenever fuel
becomes scarce and expensive but forget -CORRECT PRESENT TENSE AND CONDITIONAL WHENEVER