Answer
(a). $\frac{1-a^{2}}{a}$
(b). $\frac{\cos^{2}\theta}{\sin\theta}$
Work Step by Step
(a). Given expression is-
$\frac{1}{a} - a$
= $\frac{1}{a} - a\times\frac{a}{a}$
= $\frac{1}{a} - \frac{a^{2}}{a}$
= $\frac{1-a^{2}}{a}$
(b). Given expression is-
$\frac{1}{\sin\theta} -\sin\theta$
= $\frac{1}{\sin\theta} - \sin\theta\times\frac{\sin\theta}{\sin\theta}$
= $\frac{1}{\sin\theta} - \frac{\sin^{2}\theta}{\sin\theta}$
= $\frac{1-\sin^{2}\theta}{\sin\theta}$
= $\frac{\cos^{2}\theta}{\sin\theta}$
[ From first Pythagorean identity, $ (1 - \sin^{2}\theta)$ can be written as $\cos^{2}\theta$]
