1. Make tanT for the first equation the subject.
2. Make secT for the second equation the subject.
3. Sub into 1 + tan^2 T = sec^2 T
To turn parametric equations into a cartesian equation, you always need to eliminate the parameters.
This can be done by simply subbing, where it's something simple like x+p=5 and py = 15
or be subbed into an identity such as the trigonometry identities and p^2 + q^2 = (p+q)^2 - 2pq.
Post again if that isn't enough help.