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If $(\sec A + \tan A)(1 - \sin A) = k \cos A$, then find the value of $k$.
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$\left( \frac{1}{\cos A} + \frac{\sin A}{\cos A} \right) (1 - \sin A) = k \cos A \Rightarrow 1 - \sin^2 A = k \cos^2 A \Rightarrow \cos^2 A = k \cos^2 A \Rightarrow k = 1$. ($\frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2}$ marks)