\({\left(\sqrt[3]{(\left(\sin \varepsilon\right) * \left(\cos x\right) + \left(\sin x \cdot \left(\cos \varepsilon - 1\right)\right))_*}\right)}^3\)
- Started with
\[\sin \left(x + \varepsilon\right) - \sin x\]
37.3
- Using strategy
rm 37.3
- Applied sin-sum to get
\[\color{red}{\sin \left(x + \varepsilon\right)} - \sin x \leadsto \color{blue}{\left(\sin x \cdot \cos \varepsilon + \cos x \cdot \sin \varepsilon\right)} - \sin x\]
22.0
- Using strategy
rm 22.0
- Applied add-cube-cbrt to get
\[\color{red}{\left(\sin x \cdot \cos \varepsilon + \cos x \cdot \sin \varepsilon\right) - \sin x} \leadsto \color{blue}{{\left(\sqrt[3]{\left(\sin x \cdot \cos \varepsilon + \cos x \cdot \sin \varepsilon\right) - \sin x}\right)}^3}\]
22.7
- Applied simplify to get
\[{\color{red}{\left(\sqrt[3]{\left(\sin x \cdot \cos \varepsilon + \cos x \cdot \sin \varepsilon\right) - \sin x}\right)}}^3 \leadsto {\color{blue}{\left(\sqrt[3]{(\left(\sin \varepsilon\right) * \left(\cos x\right) + \left(\cos \varepsilon \cdot \sin x - \sin x\right))_*}\right)}}^3\]
1.6
- Using strategy
rm 1.6
- Applied *-un-lft-identity to get
\[{\left(\sqrt[3]{(\left(\sin \varepsilon\right) * \left(\cos x\right) + \left(\cos \varepsilon \cdot \sin x - \color{red}{\sin x}\right))_*}\right)}^3 \leadsto {\left(\sqrt[3]{(\left(\sin \varepsilon\right) * \left(\cos x\right) + \left(\cos \varepsilon \cdot \sin x - \color{blue}{1 \cdot \sin x}\right))_*}\right)}^3\]
1.6
- Applied distribute-rgt-out-- to get
\[{\left(\sqrt[3]{(\left(\sin \varepsilon\right) * \left(\cos x\right) + \color{red}{\left(\cos \varepsilon \cdot \sin x - 1 \cdot \sin x\right)})_*}\right)}^3 \leadsto {\left(\sqrt[3]{(\left(\sin \varepsilon\right) * \left(\cos x\right) + \color{blue}{\left(\sin x \cdot \left(\cos \varepsilon - 1\right)\right)})_*}\right)}^3\]
1.6
