Establish the identity: $$\dfrac{\cot\theta + \sec\theta}{\cos\theta + \tan\theta} = \sec\theta \cot\theta$$
The first step I got was: $$\sec\theta \cot\theta = \dfrac{\sec\theta \cot\theta\,\big(\cos\theta + \tan\theta\big)}{\cos\theta + \tan\theta}$$
Then it tells me to rewrite the factor $$\cos\theta + \tan\theta$$ in the numerator using reciprocal identities.
How would I do that? Here is what the assignment looked like: