だが — But / However (formal written)

試験は難しかった。だが、合格した。

Shiken wa muzukashikatta. Daga, gōkaku shita.

The exam was difficult. However, I passed.

だが = but/however (formal), linking a contrast

努力はした。だが、結果は出なかった。

Doryoku wa shita. Daga, kekka wa denakatta.

I made the effort. But the results didn't come.

だが opens a formal written contrast to the prior sentence

何度も電話した。だが、だれも出なかった。

Nando mo denwa shita. Daga, dare mo denakatta.

I called many times. However, no one answered.

だが = but/however (formal), the calls went unanswered