N3
がたい
Hard to, Difficult to
あいつが言うことは信じがたいが、今は信じるしかない。
It is hard to believe what he says, but we have no choice but to trust him.
Explanation
「〜がたい」 (難い) attaches to the verb stem and means 'hard to ...'. It is about being mentally, emotionally or morally hard to do or accept, not about ability: 「信じがたい話」 (an unbelievable story) 「許しがたい行為」 (an unforgivable act). It mostly follows verbs of thought, perception or attitude: 信じる, 理解する, 許す, 受け入れる.
Mixed up with
「〜がたい」: hard to accept or do for mental or moral reasons. It cannot be used for physical difficulty: you cannot say 「この肉は硬くて食べがたい」.
「〜にくい」: difficulty caused by the nature of the thing (tough meat is hard to chew, slippery road is hard to walk).
「〜づらい」: subjectively painful or awkward (a sore throat makes it hard to swallow).
「〜かねる」 (N2): politely says you cannot, because of your position.