Initial program 12.0
\[\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]
Simplified12.0
\[\leadsto \color{blue}{\sin th \cdot \frac{\sin ky}{\sqrt{\sin kx \cdot \sin kx + \sin ky \cdot \sin ky}}}\]
- Using strategy
rm Applied *-un-lft-identity12.0
\[\leadsto \sin th \cdot \frac{\color{blue}{1 \cdot \sin ky}}{\sqrt{\sin kx \cdot \sin kx + \sin ky \cdot \sin ky}}\]
Applied associate-/l*12.0
\[\leadsto \sin th \cdot \color{blue}{\frac{1}{\frac{\sqrt{\sin kx \cdot \sin kx + \sin ky \cdot \sin ky}}{\sin ky}}}\]
- Using strategy
rm Applied *-un-lft-identity12.0
\[\leadsto \sin th \cdot \frac{1}{\frac{\sqrt{\sin kx \cdot \sin kx + \sin ky \cdot \sin ky}}{\color{blue}{1 \cdot \sin ky}}}\]
Applied *-un-lft-identity12.0
\[\leadsto \sin th \cdot \frac{1}{\frac{\sqrt{\color{blue}{1 \cdot \left(\sin kx \cdot \sin kx + \sin ky \cdot \sin ky\right)}}}{1 \cdot \sin ky}}\]
Applied sqrt-prod12.0
\[\leadsto \sin th \cdot \frac{1}{\frac{\color{blue}{\sqrt{1} \cdot \sqrt{\sin kx \cdot \sin kx + \sin ky \cdot \sin ky}}}{1 \cdot \sin ky}}\]
Applied times-frac12.0
\[\leadsto \sin th \cdot \frac{1}{\color{blue}{\frac{\sqrt{1}}{1} \cdot \frac{\sqrt{\sin kx \cdot \sin kx + \sin ky \cdot \sin ky}}{\sin ky}}}\]
Applied add-cube-cbrt12.0
\[\leadsto \sin th \cdot \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\frac{\sqrt{1}}{1} \cdot \frac{\sqrt{\sin kx \cdot \sin kx + \sin ky \cdot \sin ky}}{\sin ky}}\]
Applied times-frac12.0
\[\leadsto \sin th \cdot \color{blue}{\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{\sqrt{1}}{1}} \cdot \frac{\sqrt[3]{1}}{\frac{\sqrt{\sin kx \cdot \sin kx + \sin ky \cdot \sin ky}}{\sin ky}}\right)}\]
Simplified12.0
\[\leadsto \sin th \cdot \left(\color{blue}{1} \cdot \frac{\sqrt[3]{1}}{\frac{\sqrt{\sin kx \cdot \sin kx + \sin ky \cdot \sin ky}}{\sin ky}}\right)\]
Simplified12.0
\[\leadsto \sin th \cdot \left(1 \cdot \color{blue}{\frac{\sin ky}{\sqrt{\sin ky \cdot \sin ky + \sin kx \cdot \sin kx}}}\right)\]
Final simplification12.0
\[\leadsto \sin th \cdot \frac{\sin ky}{\sqrt{\sin ky \cdot \sin ky + \sin kx \cdot \sin kx}}\]
