Initial program 4.0
\[\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]
- Using strategy
rm Applied clear-num4.0
\[\leadsto \color{blue}{\frac{1}{\frac{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}}{\sin ky}}} \cdot \sin th\]
- Using strategy
rm Applied add-cube-cbrt4.4
\[\leadsto \frac{1}{\color{blue}{\left(\sqrt[3]{\frac{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}}{\sin ky}} \cdot \sqrt[3]{\frac{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}}{\sin ky}}\right) \cdot \sqrt[3]{\frac{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}}{\sin ky}}}} \cdot \sin th\]
Applied associate-/r*4.4
\[\leadsto \color{blue}{\frac{\frac{1}{\sqrt[3]{\frac{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}}{\sin ky}} \cdot \sqrt[3]{\frac{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}}{\sin ky}}}}{\sqrt[3]{\frac{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}}{\sin ky}}}} \cdot \sin th\]
Taylor expanded around inf 4.4
\[\leadsto \frac{\frac{1}{\sqrt[3]{\frac{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}}{\sin ky}} \cdot \sqrt[3]{\frac{\color{blue}{\sqrt{{\left(\sin ky\right)}^{2} + {\left(\sin kx\right)}^{2}}}}{\sin ky}}}}{\sqrt[3]{\frac{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}}{\sin ky}}} \cdot \sin th\]
Applied simplify4.0
\[\leadsto \color{blue}{\frac{\sin th}{\frac{\sqrt{\sin ky \cdot \sin ky + \sin kx \cdot \sin kx}}{\sin ky}}}\]
