Initial program 12.0
\[\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]
Simplified12.0
\[\leadsto \color{blue}{\sin th \cdot \frac{\sin ky}{\sqrt{\sin kx \cdot \sin kx + \sin ky \cdot \sin ky}}}\]
- Using strategy
rm Applied *-un-lft-identity12.0
\[\leadsto \sin th \cdot \frac{\color{blue}{1 \cdot \sin ky}}{\sqrt{\sin kx \cdot \sin kx + \sin ky \cdot \sin ky}}\]
Applied associate-/l*12.0
\[\leadsto \sin th \cdot \color{blue}{\frac{1}{\frac{\sqrt{\sin kx \cdot \sin kx + \sin ky \cdot \sin ky}}{\sin ky}}}\]
- Using strategy
rm Applied div-inv12.1
\[\leadsto \sin th \cdot \frac{1}{\color{blue}{\sqrt{\sin kx \cdot \sin kx + \sin ky \cdot \sin ky} \cdot \frac{1}{\sin ky}}}\]
Applied associate-/r*12.0
\[\leadsto \sin th \cdot \color{blue}{\frac{\frac{1}{\sqrt{\sin kx \cdot \sin kx + \sin ky \cdot \sin ky}}}{\frac{1}{\sin ky}}}\]
- Using strategy
rm Applied add-cube-cbrt12.1
\[\leadsto \sin th \cdot \frac{\frac{1}{\sqrt{\color{blue}{\left(\left(\sqrt[3]{\sin kx} \cdot \sqrt[3]{\sin kx}\right) \cdot \sqrt[3]{\sin kx}\right)} \cdot \sin kx + \sin ky \cdot \sin ky}}}{\frac{1}{\sin ky}}\]
Applied associate-*l*12.1
\[\leadsto \sin th \cdot \frac{\frac{1}{\sqrt{\color{blue}{\left(\sqrt[3]{\sin kx} \cdot \sqrt[3]{\sin kx}\right) \cdot \left(\sqrt[3]{\sin kx} \cdot \sin kx\right)} + \sin ky \cdot \sin ky}}}{\frac{1}{\sin ky}}\]
Final simplification12.1
\[\leadsto \frac{\frac{1}{\sqrt{\left(\sin kx \cdot \sqrt[3]{\sin kx}\right) \cdot \left(\sqrt[3]{\sin kx} \cdot \sqrt[3]{\sin kx}\right) + \sin ky \cdot \sin ky}}}{\frac{1}{\sin ky}} \cdot \sin th\]
