Resol operatornamean^3θ-3tanθ=0

$$\operatorname { an } ^ { 3 } \theta - 3 \tan \theta = 0$$

Resoleu a

$$\left\{\begin{matrix}a=\frac{\sqrt[3]{\frac{3\tan(\theta )}{\theta }}}{n}\text{, }&n\neq 0\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =\pi n_{1}+\frac{\pi }{2}\text{ and }\theta \neq 0\\a\in \mathrm{R}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =\pi n_{1}+\frac{\pi }{2}\text{ and }\left(n=0\text{ or }\theta =0\right)\text{ and }\exists n_{2}\in \mathrm{Z}\text{ : }\theta =\pi n_{2}\text{, }not(n_{2}=0)\end{matrix}\right,$$

Resoleu n

$$\left\{\begin{matrix}n=\frac{\sqrt[3]{\frac{3\tan(\theta )}{\theta }}}{a}\text{, }&a\neq 0\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =\pi n_{1}+\frac{\pi }{2}\text{ and }\theta \neq 0\\n\in \mathrm{R}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =\pi n_{1}+\frac{\pi }{2}\text{ and }\left(a=0\text{ or }\theta =0\right)\text{ and }\exists n_{2}\in \mathrm{Z}\text{ : }\theta =\pi n_{2}\text{, }not(n_{2}=0)\end{matrix}\right,$$