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