Cho

- Hướng dẫn giải

$$\begin{gathered} {\tan }^3\alpha +co{t}^3\alpha =\left(\tan \alpha +cot\alpha \right).\left({\tan }^2\alpha -\tan \alpha .cot\alpha +co{t}^2\alpha \right) \\ =4.\left[{\left(\tan \alpha +cot\alpha \right)}^2-3\tan \alpha .cot\alpha \right]=4.\left(4^2-3.1\right)=52 \end{gathered}$$