So you have a DNS server that is hosting firstdomain.com and you associated this domain with ns.firstdomain.com. so on that dns server create another primary zone for seconddomain.com. when you register this domain with godaddy, associate this domain with ns.firstdomain.com as well.
Normally, registrars want for you to specificy at least two NS servers that will be hosting your domain. having more than one NS server will improve the availability and fault tolerance of your DNS infrastructure.
JorgeM
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