Initial program 12.4
\[\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]
Simplified8.8
\[\leadsto \color{blue}{\sin th \cdot \frac{\sin ky}{\sqrt{\left(\sin kx\right)^2 + \left(\sin ky\right)^2}^*}}\]
- Using strategy
rm Applied clear-num8.8
\[\leadsto \sin th \cdot \color{blue}{\frac{1}{\frac{\sqrt{\left(\sin kx\right)^2 + \left(\sin ky\right)^2}^*}{\sin ky}}}\]
Applied un-div-inv8.8
\[\leadsto \color{blue}{\frac{\sin th}{\frac{\sqrt{\left(\sin kx\right)^2 + \left(\sin ky\right)^2}^*}{\sin ky}}}\]
- Using strategy
rm Applied clear-num8.8
\[\leadsto \frac{\sin th}{\color{blue}{\frac{1}{\frac{\sin ky}{\sqrt{\left(\sin kx\right)^2 + \left(\sin ky\right)^2}^*}}}}\]
- Using strategy
rm Applied clear-num8.8
\[\leadsto \frac{\sin th}{\frac{1}{\color{blue}{\frac{1}{\frac{\sqrt{\left(\sin kx\right)^2 + \left(\sin ky\right)^2}^*}{\sin ky}}}}}\]
Final simplification8.8
\[\leadsto \frac{\sin th}{\frac{1}{\frac{1}{\frac{\sqrt{\left(\sin kx\right)^2 + \left(\sin ky\right)^2}^*}{\sin ky}}}}\]
