が、実は

but actually

→ が
phrase Rare #39,533
but actually Used to introduce a surprising fact that contrasts with what was just stated or what seems to be true.
JA: 彼は元気そうだったが、実は熱があった。
EN: He looked well, but actually he had a fever.

その男の子は病気には見えないが、実は病気だ

That boy doesn't look sick, but he actually is.

の方が殴った彼女は言っているが、実はその逆だった

She says her husband hit her, but in fact, it was the other way around.

彼は教師をしているが、実はスパイ

He is a teacher, but in reality, he is a spy.

彼は落ち着いて見えたが、実はとても緊張していた

He looked calm, but he was actually very nervous.