i-adjective
unbelievable; incredible; implausible
Expresses that something is hard to believe or accept as true, often due to being surprising, shocking, or contrary to expectation.
彼の話はあまりに信じがたい内容だった。
His story was too unbelievable to accept.
そのニュースは信じがたいほど衝撃的だった。
The news was so shocking it was hard to believe.
信じられない is more common in everyday speech and can express disbelief or amazement. 信じがたい is slightly more formal and emphasizes the difficulty of believing something.
Compound of 信じる (to believe) and the suffix がたい (hard to do), from the classical adjective 難し (かたし).