Initial program 0.1
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
- Using strategy
rm Applied add-sqr-sqrt0.1
\[\leadsto \sin \left({\color{blue}{\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}} \cdot \sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}}^{\left(b - a\right)}\right)\]
Applied unpow-prod-down0.1
\[\leadsto \sin \color{blue}{\left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)}\]
Taylor expanded around -inf 0.1
\[\leadsto \sin \color{blue}{\left({\left(e^{\log \left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\frac{1}{4}}\right) \cdot \left(b - a\right)}\right)}^{2}\right)}\]
Simplified0.1
\[\leadsto \sin \color{blue}{\left(\sqrt{{\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(b - a\right)}}\right)}\]
- Using strategy
rm Applied add-cube-cbrt0.1
\[\leadsto \sin \left(\sqrt{{\left(\tan^{-1}_* \frac{b}{b}\right)}^{\color{blue}{\left(\left(\sqrt[3]{b - a} \cdot \sqrt[3]{b - a}\right) \cdot \sqrt[3]{b - a}\right)}}}\right)\]
Applied pow-unpow0.1
\[\leadsto \sin \left(\sqrt{\color{blue}{{\left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\sqrt[3]{b - a} \cdot \sqrt[3]{b - a}\right)}\right)}^{\left(\sqrt[3]{b - a}\right)}}}\right)\]
Final simplification0.1
\[\leadsto \sin \left(\sqrt{{\left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\sqrt[3]{b - a} \cdot \sqrt[3]{b - a}\right)}\right)}^{\left(\sqrt[3]{b - a}\right)}}\right)\]
