Initial program 12.2
\[\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]
- Using strategy
rm Applied div-inv12.3
\[\leadsto \color{blue}{\left(\sin ky \cdot \frac{1}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}}\right)} \cdot \sin th\]
Applied associate-*l*12.3
\[\leadsto \color{blue}{\sin ky \cdot \left(\frac{1}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\right)}\]
- Using strategy
rm Applied pow112.3
\[\leadsto \sin ky \cdot \left(\frac{1}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \color{blue}{{\left(\sin th\right)}^{1}}\right)\]
Applied pow112.3
\[\leadsto \sin ky \cdot \left(\color{blue}{{\left(\frac{1}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}}\right)}^{1}} \cdot {\left(\sin th\right)}^{1}\right)\]
Applied pow-prod-down12.3
\[\leadsto \sin ky \cdot \color{blue}{{\left(\frac{1}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\right)}^{1}}\]
Simplified12.2
\[\leadsto \sin ky \cdot {\color{blue}{\left(\frac{\sin th}{\sqrt{\sin ky \cdot \sin ky + \sin kx \cdot \sin kx}}\right)}}^{1}\]
Final simplification12.2
\[\leadsto \sin ky \cdot \frac{\sin th}{\sqrt{\sin kx \cdot \sin kx + \sin ky \cdot \sin ky}}\]
