Answer
(a). $\frac{b^{2}+a}{ab}$
(b). $\frac{\cos^{2}\theta+\sin\theta}{\sin\theta\cos\theta}$
Work Step by Step
(a). Given expression is-
$\frac{b}{a} + \frac{1}{b}$
= $\frac{b}{b}\times\frac{b}{a} + \frac{1}{b}\times\frac{a}{a}$
= $\frac{b^{2}}{ab} + \frac{a}{ab}$
= $\frac{b^{2}+a}{ab}$
(b). Given expression is-
$\frac{\cos\theta}{\sin\theta} + \frac{1}{\cos\theta}$
= $\frac{\cos\theta}{\cos\theta}\times\frac{\cos\theta}{\sin\theta} + \frac{1}{\cos\theta}\times\frac{\sin\theta}{\sin\theta}$
= $\frac{\cos^{2}\theta}{\sin\theta\cos\theta} + \frac{\sin\theta}{\sin\theta\cos\theta}$
= $\frac{\cos^{2}\theta+\sin\theta}{\sin\theta\cos\theta}$
