can a arcanist take wizard and sorcerer feats since its considered a parent class?
No. To get that kind of benefit they need to have an ability like the Brawler has.
Martial Training (Ex): At 1st level, a brawler counts her total brawler levels as both fighter levels and monk levels for the purpose of qualifying for feats. She also counts as both a fighter and a monk for feats and magic items that have different effects based on whether the character has levels in those classes (such as Stunning Fist and a monk’s robe). This ability does not automatically grant feats normally granted to fighters and monks based on class level, namely Stunning Fist.
If you’re talking about Arcane Discoveries, an arcanist can take them as an Arcanist Exploit using half their arcanist level as their wizard level to determine whether they qualify.
And only once, as there is no language that allows it to be taken repeatedly. The Exploit class feature explicitly states: "An arcanist exploit cannot be selected more than once."
If you want to take Arcane Exploits as an Arcanist, use the Magaambyan Initiate archetype, as the Spell Mastery feature they get at 5th level qualifies them for feats as a wizard equal to their level.