\(\frac{{\left(\sin x \cdot \cos \varepsilon\right)}^2 - \frac{{\left({\left(\cos x \cdot \sin \varepsilon\right)}^2 - {\left(\sin x\right)}^2\right)}^2}{{\left(\cos x \cdot \sin \varepsilon + \sin x\right)}^2}}{\sin x \cdot \cos \varepsilon - \left(\cos x \cdot \sin \varepsilon - \sin x\right)}\)
- Started with
\[\sin \left(x + \varepsilon\right) - \sin x\]
16.9
- Using strategy
rm 16.9
- Applied sin-sum to get
\[\color{red}{\sin \left(x + \varepsilon\right)} - \sin x \leadsto \color{blue}{\left(\sin x \cdot \cos \varepsilon + \cos x \cdot \sin \varepsilon\right)} - \sin x\]
6.4
- Applied associate--l+ to get
\[\color{red}{\left(\sin x \cdot \cos \varepsilon + \cos x \cdot \sin \varepsilon\right) - \sin x} \leadsto \color{blue}{\sin x \cdot \cos \varepsilon + \left(\cos x \cdot \sin \varepsilon - \sin x\right)}\]
6.4
- Using strategy
rm 6.4
- Applied flip-+ to get
\[\color{red}{\sin x \cdot \cos \varepsilon + \left(\cos x \cdot \sin \varepsilon - \sin x\right)} \leadsto \color{blue}{\frac{{\left(\sin x \cdot \cos \varepsilon\right)}^2 - {\left(\cos x \cdot \sin \varepsilon - \sin x\right)}^2}{\sin x \cdot \cos \varepsilon - \left(\cos x \cdot \sin \varepsilon - \sin x\right)}}\]
6.4
- Using strategy
rm 6.4
- Applied flip-- to get
\[\frac{{\left(\sin x \cdot \cos \varepsilon\right)}^2 - {\color{red}{\left(\cos x \cdot \sin \varepsilon - \sin x\right)}}^2}{\sin x \cdot \cos \varepsilon - \left(\cos x \cdot \sin \varepsilon - \sin x\right)} \leadsto \frac{{\left(\sin x \cdot \cos \varepsilon\right)}^2 - {\color{blue}{\left(\frac{{\left(\cos x \cdot \sin \varepsilon\right)}^2 - {\left(\sin x\right)}^2}{\cos x \cdot \sin \varepsilon + \sin x}\right)}}^2}{\sin x \cdot \cos \varepsilon - \left(\cos x \cdot \sin \varepsilon - \sin x\right)}\]
6.4
- Applied square-div to get
\[\frac{{\left(\sin x \cdot \cos \varepsilon\right)}^2 - \color{red}{{\left(\frac{{\left(\cos x \cdot \sin \varepsilon\right)}^2 - {\left(\sin x\right)}^2}{\cos x \cdot \sin \varepsilon + \sin x}\right)}^2}}{\sin x \cdot \cos \varepsilon - \left(\cos x \cdot \sin \varepsilon - \sin x\right)} \leadsto \frac{{\left(\sin x \cdot \cos \varepsilon\right)}^2 - \color{blue}{\frac{{\left({\left(\cos x \cdot \sin \varepsilon\right)}^2 - {\left(\sin x\right)}^2\right)}^2}{{\left(\cos x \cdot \sin \varepsilon + \sin x\right)}^2}}}{\sin x \cdot \cos \varepsilon - \left(\cos x \cdot \sin \varepsilon - \sin x\right)}\]
6.4
