Albert must continue the following way to continue with the proof after the line [tex] \frac{sin^2(\theta)}{cos(\theta)}+cos(\theta) [/tex]:
[tex] \frac{sin^2(\theta)}{cos(\theta)}+cos(\theta)=\frac{sin^2(\theta)}{cos(\theta)}+cos(\theta)\times \frac{cos(\theta)}{sin(\theta)} [/tex]
=[tex] \frac{sin^2(\theta)}{cos(\theta)}+\frac{cos^2(\theta)}{cos(\theta)} [/tex]
=[tex] \frac{{sin^2(\theta)}+cos^2(\theta)}{cos(\theta)} [/tex]
=[tex] \frac{1}{cos(\theta)} [/tex]
[tex] =sec(\theta) [/tex] which is the required answer.
Thus, as we can see, after the given line in the question, Albert should write [tex] cos(\theta)=cos^2(\theta)/cos(\theta) [/tex] or [tex] \frac{cos^2(theta)}{cos(theta)} [/tex] to find a common denominator.
Thus, Option B is the correct answer.
