
versuchen
to try
To begin or carry out an action without being sure whether it will succeed; to make an attempt.
Ich werde versuchen, das Fahrrad selbst zu reparieren.
I will try to repair the bicycle myself.
to try / taste
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to try
To begin or carry out an action without being sure whether it will succeed; to make an attempt.
Ich werde versuchen, das Fahrrad selbst zu reparieren.
I will try to repair the bicycle myself.

to taste
To try a small amount of a food or drink in order to test its flavor.
Möchtest du mal von meinem Kuchen versuchen?
Would you like to taste some of my cake?

to tempt
(Elevated) To lead someone into temptation; to entice someone into an ill-considered or morally wrong action.
Der Teufel versuchte ihn mit Versprechungen von Reichtum und Macht.
The devil tempted him with promises of wealth and power.
The verb 'versuchen' is a combination of the prefix 'ver-' and the verb 'suchen' (to search/look for). You can think of it as 'searching' for a way or a solution in order to achieve something.
Er suchte nach einer Möglichkeit, die Tür zu öffnen, und versuchte es mit einem Draht.
He looked for a way to open the door and tried it with a piece of wire.
In its most common meaning, 'versuchen' is used with an infinitive construction. The verb is followed by a comma and then 'zu' + the infinitive of the second verb.
Ich versuche, pünktlich zu sein.
I am trying to be on time.
When 'versuchen' appears in the context of food or drink, it means 'probieren' (to try/taste). In this case, it is often used with the preposition 'von'.
Dieser Käse riecht interessant, ich muss mal davon versuchen.
This cheese smells interesting; I have to taste some of it.
The meaning 'jemanden in Versuchung führen' (to lead someone into temptation) is elevated and is mainly used in literary, philosophical, or religious texts. In everyday language, it is very rare.
Die Werbung versucht die Kunden mit Rabatten.
The advertisement tempts customers with discounts.
to cost / taste
Kosten and versuchen can both mean trying a small amount of something to check its flavor. Kosten is the specific culinary term for this. Versuchen is also possible in this context, but sounds more general.

Der Gast versucht die Suppe, bevor er sie bestellt.
The guest tastes the soup before ordering it.
Der Koch kostet die Suppe, bevor er sie serviert.
The chef tastes the soup before serving it.