Initial program 12.0
\[\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]
Simplified8.4
\[\leadsto \color{blue}{\sin th \cdot \frac{\sin ky}{\sqrt{\left(\sin kx\right)^2 + \left(\sin ky\right)^2}^*}}\]
- Using strategy
rm Applied clear-num8.4
\[\leadsto \sin th \cdot \color{blue}{\frac{1}{\frac{\sqrt{\left(\sin kx\right)^2 + \left(\sin ky\right)^2}^*}{\sin ky}}}\]
- Using strategy
rm Applied un-div-inv8.4
\[\leadsto \color{blue}{\frac{\sin th}{\frac{\sqrt{\left(\sin kx\right)^2 + \left(\sin ky\right)^2}^*}{\sin ky}}}\]
- Using strategy
rm Applied div-inv8.5
\[\leadsto \frac{\sin th}{\color{blue}{\sqrt{\left(\sin kx\right)^2 + \left(\sin ky\right)^2}^* \cdot \frac{1}{\sin ky}}}\]
Applied associate-/r*8.5
\[\leadsto \color{blue}{\frac{\frac{\sin th}{\sqrt{\left(\sin kx\right)^2 + \left(\sin ky\right)^2}^*}}{\frac{1}{\sin ky}}}\]
- Using strategy
rm Applied associate-/r/8.4
\[\leadsto \color{blue}{\frac{\frac{\sin th}{\sqrt{\left(\sin kx\right)^2 + \left(\sin ky\right)^2}^*}}{1} \cdot \sin ky}\]
Final simplification8.4
\[\leadsto \frac{\sin th}{\sqrt{\left(\sin kx\right)^2 + \left(\sin ky\right)^2}^*} \cdot \sin ky\]
