Are the earlier expansions required for The Taken King?

Yes.

What if I only own one of the two previous DLCs?
You need both The Dark Below and House of Wolves to qualify for Destiny: The Taken King – Digital Edition (source)

Here are the current ways of acquiring "The Taken King" :

• The $40 download of "The Taken King.", requiring previous DLC
• The $60 "Legendary Edition" including the original game and first two expansions, plus "The Taken King"
• The $80 "Collector's Edition"
• The $80 "Digital Collector's Edition"

(destinythegame.com)

Unfortunately, yes, you need both "The Dark Below" and "House of Wolves" expansions to play "The Taken King".