Samarbejdet bliver lettere, når vi tager hensyn til hinanden.

Because samarbejdet is the definite form of samarbejde (cooperation, the cooperation/collaboration).

• et samarbejde = a collaboration / a cooperation
• samarbejdet = the collaboration / the cooperation

In Danish, the definite article is often added to the end of the noun instead of being a separate word like the in English.

Here, bliver means becomes.

So:

• bliver lettere = becomes easier

This is a very common use of blive in Danish when something changes state:

• Det bliver koldt. = It gets cold / It becomes cold.
• Han bliver træt. = He gets tired.

So in this sentence, the idea is that cooperation becomes easier.

Because lettere is the comparative form of let.

• let = easy / light
• lettere = easier
• lettest = easiest

Since the sentence says cooperation becomes easier, Danish uses the comparative:

• Samarbejdet bliver lettere = Cooperation becomes easier

Here, når means when.

It introduces a clause explaining under what circumstances cooperation becomes easier:

• når vi tager hensyn til hinanden = when we show consideration for each other

A useful distinction:

• når is often used for something that happens generally or repeatedly, or for something expected to happen
• da is usually used for a specific event in the past

So this sentence expresses a general truth: cooperation becomes easier when we take each other into account.

Because after når, Danish uses normal subordinate clause word order.

In this clause:

• vi = subject
• tager = verb

So:

• når vi tager hensyn til hinanden

That is normal.

The important word-order rule to remember is that in main clauses, Danish often puts the verb in second position. But in subordinate clauses introduced by words like når, fordi, at, the structure is more straightforward.

If the når clause came first, the main clause would invert:

• Når vi tager hensyn til hinanden, bliver samarbejdet lettere.

Notice that bliver comes before samarbejdet in the main clause after the fronted subordinate clause.

Tage hensyn til is a fixed expression meaning:

• to take into account
• to show consideration for
• to be considerate of

Word for word, it is something like take regard to, but that is not natural English. It is better to learn it as a whole phrase.

Examples:

• Du skal tage hensyn til børnene. = You must take the children into account / be considerate of the children.
• Vi tager hensyn til miljøet. = We take the environment into account.

So in your sentence, tager hensyn til hinanden means that people are being considerate toward one another.

Hinanden means each other or one another.

So:

• til hinanden = to each other / of each other, depending on the English phrasing

In this sentence:

• tage hensyn til hinanden = show consideration for each other

A key point: hinanden is used when the action is reciprocal between two or more people.

Examples:

• Vi hjælper hinanden. = We help each other.
• De kender hinanden. = They know each other.

Because os means us, while hinanden means each other.

Compare:

• De hjælper os. = They help us.
• Vi hjælper hinanden. = We help each other.

If you used os, the meaning would change. The sentence is specifically about mutual consideration, so hinanden is the correct choice.

They are related, but not exactly the same.

• samarbejde can be a noun (collaboration/cooperation) or a verb (to collaborate)
• arbejde sammen literally means work together

Examples:

• Samarbejdet fungerer godt. = The collaboration works well.
• Vi samarbejder godt. = We collaborate well.
• Vi arbejder godt sammen. = We work well together.

In your sentence, samarbejdet is a noun, so it refers to the collaboration/cooperation itself.

Yes, absolutely. That version is completely natural.

Both mean the same thing:

• Samarbejdet bliver lettere, når vi tager hensyn til hinanden.
• Når vi tager hensyn til hinanden, bliver samarbejdet lettere.

The difference is mainly focus:

• Starting with Samarbejdet bliver lettere puts the focus first on the result.
• Starting with Når vi tager hensyn til hinanden puts the condition first.

Remember that when the subordinate clause comes first, the main clause uses inversion:

• Når vi tager hensyn til hinanden, bliver samarbejdet lettere.

not

• Når vi tager hensyn til hinanden, samarbejdet bliver lettere.

A careful approximation is:

SAM-ar-bye-det BLEE-ver LEHT-tere, nor vee TAH-ger HEN-syn til HIN-an-den

A few useful notes:

• samarbejdet: the j is like English y
• bliver: often sounds a bit like blee-ver
• lettere: the tt does not sound like a strong English t; Danish consonants are often softer
• når: the vowel is different from English nor, but that is a rough guide
• hensyn: the second part does not sound exactly like English seen, but that can help as a first approximation
• hinanden: stress is usually on the first syllable

If you are learning pronunciation, it is especially helpful to listen to native audio, because Danish pronunciation is often less phonetic than the spelling suggests.

It is neutral and natural. You could use it in many situations:

• workplace communication
• school or group work
• advice about teamwork
• general discussion about relationships and cooperation

It is not especially formal, but it is also not casual slang. It sounds like standard, good Danish.

Yes. Hensyn appears in several useful expressions. Some common ones are:

• tage hensyn til = take into account / show consideration for
• af hensyn til = out of consideration for / for the sake of
• vise hensyn = show consideration

Examples:

• Af hensyn til naboerne skal vi være stille. = For the sake of the neighbours, we must be quiet.
• Hun viser altid hensyn. = She always shows consideration.

So hensyn is a very useful word connected with politeness, empathy, and practical consideration.