Choose the correct option. Justify your choice.

(sec A + tan A) (1 – sin A) =

1. sec A

2. sin A

3. cosec A

4. cos A

Solving,

$\Rightarrow \text{(sec A + tan A) (1 – sin A)} \\[1em] \Rightarrow \Big(\dfrac{1}{\text{cos A}} + \dfrac{\text{sin A}}{\text{cos A}}\Big)\text{(1 - sin A)} \\[1em] \Rightarrow \Big(\dfrac{\text{1 + sin A}}{\text{cos A}}\Big)\text{(1 - sin A)} \\[1em] \Rightarrow \dfrac{\text{1 - sin}^2 A}{\text{cos A}} \\[1em] \Rightarrow \dfrac{\text{cos}^2 A}{\text{cos A}} \\[1em] \Rightarrow \text{cos A}.$

Hence, Option 4 is the correct option.