Learn Hardcore Polish: Ten taniec jest trudny, ale ona tańczy coraz lepiej. - This dance is difficult, but she dances better and better.

ten taniec – literally this dance; ten is the masculine singular demonstrative that must agree with taniec (a masculine noun).
tamten taniec – that dance (over there); adds a stronger sense of physical or figurative distance.
to – is a neuter form (matching a neuter noun like to dziecko – this child) or can be a general this/it in To jest trudne (This/That is difficult).

You can’t say *to taniec in this sentence because taniec is masculine, and determiners must agree in gender, number, and case. So:

ten taniec ✅ (this dance – masculine)
to dziecko ✅ (this child – neuter)
to jest trudne ✅ (this/that is difficult – neutral “it”)

What case is ten taniec in, and how can I recognize it?

Ten taniec is in the nominative singular case.

Clues:

It’s the subject of the sentence:
Ten taniec jest trudny. → This dance is difficult.
The basic “dictionary form” (nominative singular) of the noun taniec appears unchanged.
The demonstrative ten is also in nominative singular masculine, agreeing with taniec.

If we changed the function, the endings and demonstrative would change:

Widzę ten taniec. – I see this dance. (accusative, but same form for inanimate masculine)
Nie ma tego tańca. – There is no (of) this dance. (genitive: tego tańca)

Here it’s clearly the subject, so nominative.

Why is it jest trudny and not jest trudne or jest trudna?

The adjective trudny (difficult) must agree with the noun taniec in:

gender – taniec is masculine
number – singular here
case – nominative in this sentence

So:

ten taniec jest trudny – this dance is difficult (masc. sg.)
ta piosenka jest trudna – this song is difficult (fem. sg.)
to ćwiczenie jest trudne – this exercise is difficult (neuter sg.)
te tańce są trudne – these dances are difficult (plural)

Using trudne or trudna would mismatch the masculine noun taniec.

Could I also say To jest trudny taniec instead of Ten taniec jest trudny? Is there a difference?

Yes, both are grammatically correct, but the emphasis is slightly different.

Ten taniec jest trudny.
Literally: This dance is difficult.
– Focus starts on this particular dance (which we’re talking about) and then tells us its quality.
To jest trudny taniec.
Literally: This/That is a difficult dance.
– Starts with a neutral To (“this/that/it”) and then classifies it: it is a difficult dance.

In many contexts they’re interchangeable, but:

Ten taniec jest trudny feels more like “You see this dance we’re talking about? It’s difficult.”
To jest trudny taniec feels more like introducing or identifying it: “What is this? It’s a difficult dance.”

Why is ona used here? Could I just say …ale tańczy coraz lepiej without the pronoun?

Yes, you can usually omit personal pronouns in Polish because the verb ending already shows the person:

ona tańczy – she dances / she is dancing
tańczy – (she) dances / is dancing – “she” is understood from context

So:

Ten taniec jest trudny, ale ona tańczy coraz lepiej.
Ten taniec jest trudny, ale tańczy coraz lepiej.

Both are correct. The version with ona can:

add clarity if more than one person is being discussed
add emphasis: she (specifically) is dancing better and better, maybe in contrast to others.

What tense and aspect is tańczy, and how is it formed?

Tańczy is:

Present tense
3rd person singular (he/she/it)
From the imperfective verb tańczyć (to dance).

Partial present conjugation of tańczyć:

(ja) tańczę – I dance / I am dancing
(ty) tańczysz – you dance
(on/ona/ono) tańczy – he/she/it dances
(my) tańczymy – we dance
(wy) tańczycie – you (pl.) dance
(oni/one) tańczą – they dance

Being imperfective, tańczyć is used for:

ongoing actions: Ona tańczy. – She is dancing.
repeated actions: Ona często tańczy. – She often dances.
gradual improvement: Ona tańczy coraz lepiej.

A perfective partner (used for single, complete events) is zatańczyć (to dance once, to perform a dance).

What does coraz mean, and how does coraz lepiej work grammatically?

Coraz is an adverb that expresses gradual change, roughly “more and more” or “increasingly”.

coraz lepiej = better and better / more and more better / increasingly well

Structure:

coraz
- comparative form (adjective or adverb)

Examples:

coraz lepiej – better and better
coraz gorzej – worse and worse
coraz szybciej – faster and faster
coraz trudniejszy – more and more difficult (adjective)

In the sentence:

ona tańczy coraz lepiej – she dances better and better / increasingly well.

Why is it lepiej and not lepszy in ona tańczy coraz lepiej?

Because we’re describing how she dances (the manner of the action), we need an adverb, not an adjective.

dobrze – well (adverb)
lepiej – better (adverb, comparative of dobrze)
najlepiej – best (superlative adverb)

Adjectives, on the other hand, describe nouns:

dobry taniec – a good dance (adjective)
lepszy taniec – a better dance (comparative adjective)
najlepszy taniec – the best dance (superlative adjective)

In ona tańczy coraz lepiej, we’re modifying the verb tańczy, so we need the adverb lepiej, not the adjective lepszy.

Compare:

To jest lepszy taniec. – This is a better dance. (adjective)
Ona tańczy lepiej. – She dances better. (adverb)

Can I say Ten taniec jest trudny, ale ona tańczy go coraz lepiej? What does go do?

Yes, that sentence is also correct and perfectly natural:

Ten taniec jest trudny, ale ona tańczy go coraz lepiej.
→ This dance is difficult, but she dances it better and better.

Here, go is the object pronoun “him/it” (masculine, accusative), referring back to ten taniec.

Nuance:

…ale ona tańczy coraz lepiej.
Focuses more on her general dancing skill in the context of this dance.
…ale ona tańczy go coraz lepiej.
Explicitly focuses on this particular dance – she performs this dance better and better.

Both are natural; adding go makes the reference to the specific dance more concrete.

Could the word order be Ten taniec jest trudny, ale coraz lepiej tańczy? Does it change the meaning?

Yes, that’s also grammatically correct:

Ten taniec jest trudny, ale coraz lepiej tańczy.

Meaning is essentially the same: This dance is difficult, but she dances better and better.

However, Polish word order is flexible and used for emphasis:

…ale ona tańczy coraz lepiej.
Slight emphasis on ona (she in contrast to others, or she as the topic).
…ale tańczy coraz lepiej.
Neutral, natural flow.
…ale coraz lepiej tańczy.
Slight emphasis on coraz lepiej – “the important thing is that (she) is dancing better and better.”

Context and intonation decide which part is highlighted.

Why is the conjunction ale used here? Could I use chociaż or jednak instead?

Ale means but and introduces a contrast:

Ten taniec jest trudny, ale ona tańczy coraz lepiej.
→ This dance is difficult, but she dances better and better.

Alternatives:

chociaż – although / even though
Typically starts a subordinate clause:
- Chociaż ten taniec jest trudny, ona tańczy coraz lepiej.
  → Although this dance is difficult, she dances better and better.
jednak – however / nevertheless
Adverb/conjunction used to stress contrast:
- Ten taniec jest trudny, jednak ona tańczy coraz lepiej.
  → This dance is difficult; however, she dances better and better.

So ale = simple “but”; chociaż creates a concessive “although” clause; jednak adds a stronger “nevertheless” feeling. All are possible, but ale is the most neutral and common here.