The cautious trainer carefully approached the cage where the bear was sleeping.
Alright, so let's go through each of the choices.
A) The word cautious is spelled incorrectly.
Is the word "cautious" spelled incorrectly? No. So, it's not A.
B) The verb tense is inconsistent throughout the sentence.
The two verb phrases are "approached" and "was sleeping." Both are in past tense, though one is progressive, so they are fine. It's not B, either.
C) The sentence is redundant; it is unnecessarily repetitive.
Is there anything about the sentence that repeats itself? What about "cautious" and "carefully"? They are both saying the same thing. So this would be the correct answer.
D) The sentence has a misplaced modifier in the second clause.
Is there a modifier in the second clause? (A modifier is a word that can be removed from the sentence and it will still make sense. It adds details.) No, so it's not D.