wirksam
effective
Showing an effect; having an effect. Often refers to measures, medicines, or actions that achieve a desired result.
Das neue Medikament ist sehr wirksam gegen Kopfschmerzen.
The new medication is very effective against headaches.

effective / valid
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effective
Showing an effect; having an effect. Often refers to measures, medicines, or actions that achieve a desired result.
Das neue Medikament ist sehr wirksam gegen Kopfschmerzen.
The new medication is very effective against headaches.

The adjective 'wirksam' (effective/valid) is derived from the verb 'wirken' (to have an effect). The ending '-sam' forms adjectives and means something like 'having the ability to...'. So 'wirksam' literally means that something has the ability to have an effect.
Diese Methode ist einfach, aber sehr wirksam.
This method is simple but very effective.
You can recognize the meaning of 'wirksam' (effective/valid) from the context. In connection with medicine, measures, or strategies, it means 'effective'. In a legal or administrative context (contracts, laws, terminations), it means 'legally valid'.
Die neue Werbekampagne war sehr wirksam.
The new advertising campaign was very effective.
In the meaning 'effective', 'wirksam' is often used with the preposition 'gegen' (against). Typical combinations are 'ein wirksames Mittel gegen etwas' (an effective remedy for/against something), 'wirksame Maßnahmen' (effective measures), or 'ein wirksamer Schutz' (effective protection).
Gibt es ein wirksames Mittel gegen Mückenstiche?
Is there an effective remedy for mosquito bites?
In legal contexts, the formulation 'wirksam werden' (to become valid/take effect) is very common. It means that something (e.g., a law or contract) comes into force or becomes valid.
Die neue Regelung wird am 1. Januar wirksam.
The new regulation becomes valid on January 1.
active
'aktiv' and 'wirksam' can both be used for things that are not just present, but do something or apply. 'aktiv' means that something is switched on, in operation, or currently functioning. 'wirksam' means that something has an effect or is legally valid. So a system can be 'aktiv' without a measure already being 'wirksam'. Learners may confuse the words because both are sometimes connected with 'in Kraft' (in force) or 'funktionierend' (functioning). Remember: 'aktiv' is more about the state, while 'wirksam' is about the effect or validity.

Das Medikament ist wirksam und senkt das Fieber schnell.
The medication is effective and lowers the fever quickly.
Die Alarmanlage ist nachts aktiv.
The alarm system is active at night.