Answer
(a). $\frac{a^{2}-b^{2}}{ab}$
(b). $\frac{\sin^{2}\theta-\cos^{2}\theta}{\sin\theta\cos\theta}$
Work Step by Step
(a). Given expression is-
$\frac{a}{b} - \frac{b}{a}$
= $\frac{a}{a}\times\frac{a}{b} - \frac{b}{a}\times\frac{b}{b}$
= $\frac{a^{2}}{ab} - \frac{b^{2}}{ab}$
= $\frac{a^{2}-b^{2}}{ab}$
(b). Given expression is-
$\frac{\sin\theta}{\cos\theta} - \frac{\cos\theta}{\sin\theta}$
= $\frac{\sin\theta}{\sin\theta}\times\frac{\sin\theta}{\cos\theta} - \frac{\cos\theta}{\sin\theta}\times\frac{\cos\theta}{\cos\theta}$
= $\frac{\sin^{2}\theta}{\sin\theta\cos\theta} - \frac{\cos^{2}\theta}{\sin\theta\cos\theta}$
= $\frac{\sin^{2}\theta-\cos^{2}\theta}{\sin\theta\cos\theta}$
