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.

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 food or drink. In this sense, they are very similar. 'kosten' fits especially well when you want to check the flavor, for example with soup, wine, or cake. 'versuchen' can also be used with this meaning, but it is easy to confuse because it much more often means trying or attempting to do something. In addition, 'kosten' also has the meaning 'to cost / to have a price'. So the context must clearly show whether it is about tasting or about money.

Am Wochenende versucht der Arzt den Kuchen, den seine Tochter gebacken hat.
On the weekend, the doctor tastes the cake that his daughter baked.
Möchtest du die Suppe kurz kosten, bevor ich Salz dazugebe?
Would you like to taste the soup quickly before I add salt?