Question

Which one does it simplify to? please

Answer 1

`1 + { \sin} \theta`

Explanation:

`\frac{ { \cos}^(2) \theta}{1 - \sin \theta} \\ \\ = \frac{ { \cos}^(2) \theta}{(1 - \sin \theta)} * ((1 + \sin \theta))/((1 + \sin \theta)) \\ \\ = \frac{{ \cos}^(2) \theta(1 + { \sin} \theta)}{(1 - { \sin}^(2) \theta)} \\ \\ = \frac{{ \cancel{ \cos}^(2) \theta}(1 + { \sin} \theta)}{ \cancel{{ \cos}^(2) \theta}} \\ \\ = 1 + { \sin} \theta`

Answer 2

Let's see

`\\ \rm\Rrightarrow (cos^2\theta)/(1-sin\theta)`

`\\ \rm\Rrightarrow (1-sin^2\theta)/(1-sin\theta)`

• (a+b)(a-b)=a²-b²

`\\ \rm\Rrightarrow ((1-sin\theta)(1+sin\theta))/(1-sin\theta)`[/tex]

`\\ \rm\Rrightarrow 1+sin\theta`

Option A