(sec A + tan A)(1 - sin A) is equal to

1. sec A

2. sin A

3. cosec A

4. cos A

Given, (sec A + tan A)(1 - sin A)

On solving,

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

Hence, Option 4 is the correct option.