Initial program 4.1
\[\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]
- Using strategy
rm Applied add-cube-cbrt4.4
\[\leadsto \frac{\sin ky}{\sqrt{{\color{blue}{\left(\left(\sqrt[3]{\sin kx} \cdot \sqrt[3]{\sin kx}\right) \cdot \sqrt[3]{\sin kx}\right)}}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]
Applied unpow-prod-down4.4
\[\leadsto \frac{\sin ky}{\sqrt{\color{blue}{{\left(\sqrt[3]{\sin kx} \cdot \sqrt[3]{\sin kx}\right)}^{2} \cdot {\left(\sqrt[3]{\sin kx}\right)}^{2}} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]
Applied simplify4.2
\[\leadsto \frac{\sin ky}{\sqrt{\color{blue}{\left(\sin kx \cdot \sqrt[3]{\sin kx}\right)} \cdot {\left(\sqrt[3]{\sin kx}\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]
- Using strategy
rm Applied add-cube-cbrt4.2
\[\leadsto \frac{\sin ky}{\sqrt{\left(\sin kx \cdot \sqrt[3]{\color{blue}{\left(\sqrt[3]{\sin kx} \cdot \sqrt[3]{\sin kx}\right) \cdot \sqrt[3]{\sin kx}}}\right) \cdot {\left(\sqrt[3]{\sin kx}\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]
Applied cbrt-prod4.3
\[\leadsto \frac{\sin ky}{\sqrt{\left(\sin kx \cdot \color{blue}{\left(\sqrt[3]{\sqrt[3]{\sin kx} \cdot \sqrt[3]{\sin kx}} \cdot \sqrt[3]{\sqrt[3]{\sin kx}}\right)}\right) \cdot {\left(\sqrt[3]{\sin kx}\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]
