Initial program 3.8
\[\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]
- Using strategy
rm Applied add-sqr-sqrt3.8
\[\leadsto \frac{\sin ky}{\sqrt{\color{blue}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}} \cdot \sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}}}} \cdot \sin th\]
Applied sqrt-prod4.1
\[\leadsto \frac{\sin ky}{\color{blue}{\sqrt{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sqrt{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}}}} \cdot \sin th\]
Applied simplify4.1
\[\leadsto \frac{\sin ky}{\color{blue}{\sqrt{\sqrt{\left(\sin kx\right)^2 + \left(\sin ky\right)^2}^*}} \cdot \sqrt{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}}} \cdot \sin th\]
Applied simplify0.6
\[\leadsto \frac{\sin ky}{\sqrt{\sqrt{\left(\sin kx\right)^2 + \left(\sin ky\right)^2}^*} \cdot \color{blue}{\sqrt{\sqrt{\left(\sin kx\right)^2 + \left(\sin ky\right)^2}^*}}} \cdot \sin th\]
- Using strategy
rm Applied div-inv0.6
\[\leadsto \color{blue}{\left(\sin ky \cdot \frac{1}{\sqrt{\sqrt{\left(\sin kx\right)^2 + \left(\sin ky\right)^2}^*} \cdot \sqrt{\sqrt{\left(\sin kx\right)^2 + \left(\sin ky\right)^2}^*}}\right)} \cdot \sin th\]
Applied associate-*l*0.6
\[\leadsto \color{blue}{\sin ky \cdot \left(\frac{1}{\sqrt{\sqrt{\left(\sin kx\right)^2 + \left(\sin ky\right)^2}^*} \cdot \sqrt{\sqrt{\left(\sin kx\right)^2 + \left(\sin ky\right)^2}^*}} \cdot \sin th\right)}\]
Applied simplify0.3
\[\leadsto \sin ky \cdot \color{blue}{\frac{\sin th}{\sqrt{\left(\sin kx\right)^2 + \left(\sin ky\right)^2}^*}}\]
