Answer
See below.
Work Step by Step
Using the learned identities: $\sec \theta- \cos\theta=\frac{1}{\cos \theta}-\frac{\cos^2 \theta}{\cos \theta}=\frac{1-\cos^2 \theta}{\cos \theta}=\frac{\sin^2 \theta}{\cos \theta}=\sin\theta\tan\theta$
Hence we proved what we had to.