$\begin{align}  & \cot \alpha (\sec \alpha +\operatorname{cosec}\alpha )=\left( \frac{\cos \alpha }{\sin \alpha } \right)\left( \frac{1}{\cos \alpha }+\frac{1}{\sin \alpha } \right) \\ & \cot \alpha (\sec \alpha +\operatorname{cosec}\alpha )=\frac{1}{\sin \alpha }+\frac{\cos \alpha }{{{\sin }^{2}}\alpha } \\ & \cot \alpha (\sec \alpha +\operatorname{cosec}\alpha )=\operatorname{cosec}\alpha +\frac{\cos \alpha }{\sin \alpha \cdot \sin \alpha } \\ & \cot \alpha (\sec \alpha +\operatorname{cosec}\alpha )=\operatorname{cosec}\alpha +\text{cosec}\alpha \text{cot}\alpha  \\\end{align}$