Initial program 12.5
\[\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]
Simplified11.4
\[\leadsto \color{blue}{\frac{\sin th \cdot \sin ky}{\sqrt{\left(\sin kx\right)^2 + \left(\sin ky\right)^2}^*}}\]
- Using strategy
rm Applied *-un-lft-identity11.4
\[\leadsto \frac{\sin th \cdot \sin ky}{\color{blue}{1 \cdot \sqrt{\left(\sin kx\right)^2 + \left(\sin ky\right)^2}^*}}\]
Applied times-frac9.0
\[\leadsto \color{blue}{\frac{\sin th}{1} \cdot \frac{\sin ky}{\sqrt{\left(\sin kx\right)^2 + \left(\sin ky\right)^2}^*}}\]
Simplified9.0
\[\leadsto \color{blue}{\sin th} \cdot \frac{\sin ky}{\sqrt{\left(\sin kx\right)^2 + \left(\sin ky\right)^2}^*}\]
- Using strategy
rm Applied expm1-log1p-u9.0
\[\leadsto \sin th \cdot \color{blue}{(e^{\log_* (1 + \frac{\sin ky}{\sqrt{\left(\sin kx\right)^2 + \left(\sin ky\right)^2}^*})} - 1)^*}\]
- Using strategy
rm Applied pow19.0
\[\leadsto \sin th \cdot \color{blue}{{\left((e^{\log_* (1 + \frac{\sin ky}{\sqrt{\left(\sin kx\right)^2 + \left(\sin ky\right)^2}^*})} - 1)^*\right)}^{1}}\]
Applied pow19.0
\[\leadsto \color{blue}{{\left(\sin th\right)}^{1}} \cdot {\left((e^{\log_* (1 + \frac{\sin ky}{\sqrt{\left(\sin kx\right)^2 + \left(\sin ky\right)^2}^*})} - 1)^*\right)}^{1}\]
Applied pow-prod-down9.0
\[\leadsto \color{blue}{{\left(\sin th \cdot (e^{\log_* (1 + \frac{\sin ky}{\sqrt{\left(\sin kx\right)^2 + \left(\sin ky\right)^2}^*})} - 1)^*\right)}^{1}}\]
Simplified9.0
\[\leadsto {\color{blue}{\left(\sin ky \cdot \frac{\sin th}{\sqrt{\left(\sin kx\right)^2 + \left(\sin ky\right)^2}^*}\right)}}^{1}\]
Final simplification9.0
\[\leadsto \sin ky \cdot \frac{\sin th}{\sqrt{\left(\sin kx\right)^2 + \left(\sin ky\right)^2}^*}\]
