Answer
$$\frac{1}{cos^3\space t} - \frac{1}{cos \space t}$$
Work Step by Step
$$tan^2 \space t \space sec \space t$$
Using: $tan^2 \space t + 1 = sec^2 \space t \longrightarrow tan^2 \space t = sec^2 \space t -1 $
$$(sec^2 \space t -1 )sec \space t = sec^3\space t - sec\space t$$
Using: $sec \space t = \frac{1}{cos \space t} \longrightarrow sec^3\space t = \frac{1}{cos^3 \space t}$
$$\frac{1}{cos^3\space t} - \frac{1}{cos \space t}$$
