Do use mean sec and tan of theta (θ)? This is what I think you mean.
If cscθ = 13/5, sinθ = 5/13 because cscθ = 1/sinθ.
We also know that...
cos²θ + sin²θ = 1
So...
cos²θ + (5/13)² = 1
cos²θ = 1-(5/13)²
cos²θ = 1 - 25/169
cos²θ = 144/169
cosθ = 12/13
tanθ = sinθ/cosθ
tanθ = (5/13)/(12/13) = 5/12
