Student or Learner
a. Try as he might, he couldn't open the door.
b. However hard he tried he couldn't open the door.
a. Tall as he was he couldn't reach the ceiling.
b. Though he was tall he couldn't reach the ceiling.
I was wondering whether 1a and 2a are preferred in formal language, they sound to me a little bit pretentious.
Neither can be said to be "pretentious" nor specifically "formal". They are good colloquial uses of the word and both sentences have a rhythm. It comes down to whether or not you are happy with them as sentences within the flow of a text.