N5 Lesson 5: 10/13

but・however

⚠ が can sometimes mean something closer to "and" or comma simply connecting clauses without any contrastive meaning
also sometimes the clause after が can be omitted

Structure Legend
Structure
Verb +
い-Adjective + です
Noun + です
な-Adjective + です
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[Used often in both polite speech and in writing]

Classification from least formal to the most:
[けど << けども << けれど << けれども ⇄ が]

[More information on politeness levels]

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難(むずか)しいです、頑張(がんば)ります。
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It is difficult, but I will do my best.
In an AがB sentence, unlike many other grammar points, the politeness in the A and B clauses (parts of the sentence) should match. So 難しいが、頑張る and 難しいですが、頑張ります are correct. However 難しいが、頑張ります would be considered unnatural by a great number of speakers.

みんなの日本語 I : Page 56 [CH 8]
みんなの日本語 II : Page 126 [CH 45]
[DBJG] A Dictionary of Basic Japanese Grammar : Page 120
Tae Kim's Japanese Grammar Guide : Page 110