\(\dfrac{1}{\cos^2\theta} + \dfrac{1}{\sin^2\theta} = \dfrac{\sin^2\theta + \cos^2\theta}{\sin^2\theta \cos^2\theta}\)
\(= \dfrac{1}{\sin^2\theta \cos^2\theta}\) \(\;\) [since \(\sin^2\theta + \cos^2\theta = 1\)]
\(= \dfrac{1}{\cos^2\theta} \cdot \dfrac{1}{\sin^2\theta}\)
\(= \sec^2\theta \csc^2\theta\)