1. **Problem statement:** (ক) Given that $\sec A - \tan A = \frac{2}{5}$, find the value of $\sec A + \tan A$. 2. **Formula and important rules:** Recall the identity: $$ (\sec A + \tan A)(\sec A - \tan A) = \sec^2 A - \tan^2 A = 1 $$ This is because $\sec^2 A - \tan^2 A = 1$ is a fundamental trigonometric identity. 3. **Intermediate work:** Given $\sec A - \tan A = \frac{2}{5}$, let $x = \sec A + \tan A$. Then: $$ x \times \frac{2}{5} = 1 \implies x = \frac{5}{2} $$ 4. **Explanation:** We used the identity that the product of $(\sec A + \tan A)$ and $(\sec A - \tan A)$ equals 1. Since one factor is given, we find the other by dividing 1 by the given value. **Final answer:** $$ \sec A + \tan A = \frac{5}{2} $$