\(\frac{{\left(\sqrt[3]{{\left(\sin x \cdot \cos \varepsilon\right)}^2 - {\left(\cos x \cdot \sin \varepsilon - \sin x\right)}^2}\right)}^3}{(\left(\cos \varepsilon\right) * \left(\sin x\right) + \left(\sin x\right))_* - \sin \varepsilon \cdot \cos x}\)
- Started with
\[\sin \left(x + \varepsilon\right) - \sin x\]
16.9
- Using strategy
rm 16.9
- Applied sin-sum to get
\[\color{red}{\sin \left(x + \varepsilon\right)} - \sin x \leadsto \color{blue}{\left(\sin x \cdot \cos \varepsilon + \cos x \cdot \sin \varepsilon\right)} - \sin x\]
6.2
- Applied associate--l+ to get
\[\color{red}{\left(\sin x \cdot \cos \varepsilon + \cos x \cdot \sin \varepsilon\right) - \sin x} \leadsto \color{blue}{\sin x \cdot \cos \varepsilon + \left(\cos x \cdot \sin \varepsilon - \sin x\right)}\]
6.2
- Using strategy
rm 6.2
- Applied flip-+ to get
\[\color{red}{\sin x \cdot \cos \varepsilon + \left(\cos x \cdot \sin \varepsilon - \sin x\right)} \leadsto \color{blue}{\frac{{\left(\sin x \cdot \cos \varepsilon\right)}^2 - {\left(\cos x \cdot \sin \varepsilon - \sin x\right)}^2}{\sin x \cdot \cos \varepsilon - \left(\cos x \cdot \sin \varepsilon - \sin x\right)}}\]
6.3
- Applied simplify to get
\[\frac{{\left(\sin x \cdot \cos \varepsilon\right)}^2 - {\left(\cos x \cdot \sin \varepsilon - \sin x\right)}^2}{\color{red}{\sin x \cdot \cos \varepsilon - \left(\cos x \cdot \sin \varepsilon - \sin x\right)}} \leadsto \frac{{\left(\sin x \cdot \cos \varepsilon\right)}^2 - {\left(\cos x \cdot \sin \varepsilon - \sin x\right)}^2}{\color{blue}{(\left(\cos \varepsilon\right) * \left(\sin x\right) + \left(\sin x\right))_* - \sin \varepsilon \cdot \cos x}}\]
6.3
- Using strategy
rm 6.3
- Applied add-cube-cbrt to get
\[\frac{\color{red}{{\left(\sin x \cdot \cos \varepsilon\right)}^2 - {\left(\cos x \cdot \sin \varepsilon - \sin x\right)}^2}}{(\left(\cos \varepsilon\right) * \left(\sin x\right) + \left(\sin x\right))_* - \sin \varepsilon \cdot \cos x} \leadsto \frac{\color{blue}{{\left(\sqrt[3]{{\left(\sin x \cdot \cos \varepsilon\right)}^2 - {\left(\cos x \cdot \sin \varepsilon - \sin x\right)}^2}\right)}^3}}{(\left(\cos \varepsilon\right) * \left(\sin x\right) + \left(\sin x\right))_* - \sin \varepsilon \cdot \cos x}\]
8.1
