$\sec^2\theta + \operatorname{cosec}^2\theta = ?$

Convert each term: $\sec^2\theta + \operatorname{cosec}^2\theta = \dfrac{1}{\cos^2\theta} + \dfrac{1}{\sin^2\theta} = \dfrac{\sin^2\theta + \cos^2\theta}{\sin^2\theta\cos^2\theta} = \dfrac{1}{\sin^2\theta\cos^2\theta}$. This is exactly $\sec^2\theta\cdot\operatorname{cosec}^2\theta$.