\(\frac{{\left(\sqrt[3]{{\left(\sqrt[3]{\cos x - \cot \left(\varepsilon + x\right) \cdot \sin x}\right)}^3}\right)}^3}{\cot \left(x + \varepsilon\right) \cdot \cos x}\)
- Started with
\[\tan \left(x + \varepsilon\right) - \tan x\]
36.9
- Using strategy
rm 36.9
- Applied tan-quot to get
\[\tan \left(x + \varepsilon\right) - \color{red}{\tan x} \leadsto \tan \left(x + \varepsilon\right) - \color{blue}{\frac{\sin x}{\cos x}}\]
36.9
- Applied tan-cotan to get
\[\color{red}{\tan \left(x + \varepsilon\right)} - \frac{\sin x}{\cos x} \leadsto \color{blue}{\frac{1}{\cot \left(x + \varepsilon\right)}} - \frac{\sin x}{\cos x}\]
36.9
- Applied frac-sub to get
\[\color{red}{\frac{1}{\cot \left(x + \varepsilon\right)} - \frac{\sin x}{\cos x}} \leadsto \color{blue}{\frac{1 \cdot \cos x - \cot \left(x + \varepsilon\right) \cdot \sin x}{\cot \left(x + \varepsilon\right) \cdot \cos x}}\]
36.9
- Applied simplify to get
\[\frac{\color{red}{1 \cdot \cos x - \cot \left(x + \varepsilon\right) \cdot \sin x}}{\cot \left(x + \varepsilon\right) \cdot \cos x} \leadsto \frac{\color{blue}{\cos x - \cot \left(\varepsilon + x\right) \cdot \sin x}}{\cot \left(x + \varepsilon\right) \cdot \cos x}\]
36.9
- Using strategy
rm 36.9
- Applied add-cube-cbrt to get
\[\frac{\color{red}{\cos x - \cot \left(\varepsilon + x\right) \cdot \sin x}}{\cot \left(x + \varepsilon\right) \cdot \cos x} \leadsto \frac{\color{blue}{{\left(\sqrt[3]{\cos x - \cot \left(\varepsilon + x\right) \cdot \sin x}\right)}^3}}{\cot \left(x + \varepsilon\right) \cdot \cos x}\]
36.9
- Using strategy
rm 36.9
- Applied add-cube-cbrt to get
\[\frac{{\left(\sqrt[3]{\color{red}{\cos x - \cot \left(\varepsilon + x\right) \cdot \sin x}}\right)}^3}{\cot \left(x + \varepsilon\right) \cdot \cos x} \leadsto \frac{{\left(\sqrt[3]{\color{blue}{{\left(\sqrt[3]{\cos x - \cot \left(\varepsilon + x\right) \cdot \sin x}\right)}^3}}\right)}^3}{\cot \left(x + \varepsilon\right) \cdot \cos x}\]
36.9
