If ( A + A)(1 - A) = k A , then find the value of k .

$$\begin{aligned}& \left( \frac{1}{\cos A} + \frac{\sin A}{\cos A} \right) (1 - \sin A) \\ & = k \cos A \Rightarrow 1 - \sin^2 A = k \cos^2 A \Rightarrow \cos^2 A \\ & = k \cos^2 A \Rightarrow k = 1\end{aligned}$$. ($\frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2}$ marks)