To continue Albert's proof effectively, he should focus on finding a common denominator with the terms involved.
The equation he started with is:
\[ \tan \theta \sin \theta + \cos \theta = \sec \theta \]
He later expressed \( \tan \theta \) as \( \frac{\sin \theta}{\cos \theta} \), leading to:
\[ \frac{\sin^2 \theta}{\cos \theta} + \cos \theta = \sec \theta \]
At this point, a common denominator for the left side of the equation is needed to combine the terms properly.
Since one of the terms is already expressed with \(\cos \theta\) in the denominator, the logical step would be to express \(\cos \theta\) in the same form:
He should write \( \cos \theta = \frac{\cos^2 \theta}{\cos \theta} \) to find a common denominator.
Therefore, the correct choice is:
He should write cosine theta equals start fraction cosine squared theta over cosine theta end fraction to find a common denominator.