Answer
$ \frac{1}{\sin\theta\cos\theta}$
Work Step by Step
Given expression is-
$ \frac{\cos\theta}{\sin\theta} + \frac{\sin\theta}{\cos\theta} $
= $ \frac{\cos\theta}{\cos\theta}.\frac{\cos\theta}{\sin\theta} + \frac{\sin\theta}{\cos\theta}.\frac{\sin\theta}{\sin\theta}$
= $ \frac{\cos^{2}\theta}{\sin\theta\cos\theta} + \frac{\sin^{2}\theta}{\sin\theta\cos\theta} $
= $ \frac{\cos^{2}\theta + \sin^{2}\theta}{\sin\theta\cos\theta}$
From first Pythagorean identity , substituting, $\cos^{2}\theta + \sin^{2}\theta$ = 1
Expression becomes-
= $ \frac{1}{\sin\theta\cos\theta}$
