Answer
(a). $\frac{b-a}{ab}$
(b). $\frac{\cos\theta-\sin\theta}{\sin\theta\cos\theta}$
Work Step by Step
(a). Given expression is-
$\frac{1}{a} - \frac{1}{b}$
= $\frac{b}{b}\times\frac{1}{a} - \frac{1}{b}\times\frac{a}{a}$
= $\frac{b}{ab} - \frac{a}{ab}$
= $\frac{b-a}{ab}$
(b). Given expression is-
$\frac{1}{\sin\theta} - \frac{1}{\cos\theta}$
= $\frac{\cos\theta}{\cos\theta}\times\frac{1}{\sin\theta} - \frac{1}{\cos\theta}\times\frac{\sin\theta}{\sin\theta}$
= $\frac{\cos\theta}{\sin\theta\cos\theta} - \frac{\sin\theta}{\sin\theta\cos\theta}$
= $\frac{\cos\theta-\sin\theta}{\sin\theta\cos\theta}$
