\(\frac{b}{\sqrt{c^2 + d^2}^*} \cdot \frac{c}{\sqrt{c^2 + d^2}^*} - \frac{a}{\sqrt{c^2 + d^2}^*} \cdot \frac{d}{\sqrt{c^2 + d^2}^*}\)
- Started with
\[\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\]
12.6
- Using strategy
rm 12.6
- Applied add-sqr-sqrt to get
\[\frac{b \cdot c - a \cdot d}{\color{red}{{c}^2 + {d}^2}} \leadsto \frac{b \cdot c - a \cdot d}{\color{blue}{{\left(\sqrt{{c}^2 + {d}^2}\right)}^2}}\]
12.5
- Applied simplify to get
\[\frac{b \cdot c - a \cdot d}{{\color{red}{\left(\sqrt{{c}^2 + {d}^2}\right)}}^2} \leadsto \frac{b \cdot c - a \cdot d}{{\color{blue}{\left(\sqrt{c^2 + d^2}^*\right)}}^2}\]
8.0
- Applied taylor to get
\[\frac{b \cdot c - a \cdot d}{{\left(\sqrt{c^2 + d^2}^*\right)}^2} \leadsto \frac{b \cdot c}{{\left(\sqrt{c^2 + d^2}^*\right)}^2} - \frac{d \cdot a}{{\left(\sqrt{c^2 + d^2}^*\right)}^2}\]
8.0
- Taylor expanded around 0 to get
\[\color{red}{\frac{b \cdot c}{{\left(\sqrt{c^2 + d^2}^*\right)}^2} - \frac{d \cdot a}{{\left(\sqrt{c^2 + d^2}^*\right)}^2}} \leadsto \color{blue}{\frac{b \cdot c}{{\left(\sqrt{c^2 + d^2}^*\right)}^2} - \frac{d \cdot a}{{\left(\sqrt{c^2 + d^2}^*\right)}^2}}\]
8.0
- Using strategy
rm 8.0
- Applied *-un-lft-identity to get
\[\frac{b \cdot c}{{\color{red}{\left(\sqrt{c^2 + d^2}^*\right)}}^2} - \frac{d \cdot a}{{\left(\sqrt{c^2 + d^2}^*\right)}^2} \leadsto \frac{b \cdot c}{{\color{blue}{\left(1 \cdot \sqrt{c^2 + d^2}^*\right)}}^2} - \frac{d \cdot a}{{\left(\sqrt{c^2 + d^2}^*\right)}^2}\]
8.0
- Applied square-prod to get
\[\frac{b \cdot c}{\color{red}{{\left(1 \cdot \sqrt{c^2 + d^2}^*\right)}^2}} - \frac{d \cdot a}{{\left(\sqrt{c^2 + d^2}^*\right)}^2} \leadsto \frac{b \cdot c}{\color{blue}{{1}^2 \cdot {\left(\sqrt{c^2 + d^2}^*\right)}^2}} - \frac{d \cdot a}{{\left(\sqrt{c^2 + d^2}^*\right)}^2}\]
8.0
- Applied times-frac to get
\[\color{red}{\frac{b \cdot c}{{1}^2 \cdot {\left(\sqrt{c^2 + d^2}^*\right)}^2}} - \frac{d \cdot a}{{\left(\sqrt{c^2 + d^2}^*\right)}^2} \leadsto \color{blue}{\frac{b}{{1}^2} \cdot \frac{c}{{\left(\sqrt{c^2 + d^2}^*\right)}^2}} - \frac{d \cdot a}{{\left(\sqrt{c^2 + d^2}^*\right)}^2}\]
4.3
- Applied simplify to get
\[\color{red}{\frac{b}{{1}^2}} \cdot \frac{c}{{\left(\sqrt{c^2 + d^2}^*\right)}^2} - \frac{d \cdot a}{{\left(\sqrt{c^2 + d^2}^*\right)}^2} \leadsto \color{blue}{\frac{b}{1}} \cdot \frac{c}{{\left(\sqrt{c^2 + d^2}^*\right)}^2} - \frac{d \cdot a}{{\left(\sqrt{c^2 + d^2}^*\right)}^2}\]
4.3
- Applied taylor to get
\[\frac{b}{1} \cdot \frac{c}{{\left(\sqrt{c^2 + d^2}^*\right)}^2} - \frac{d \cdot a}{{\left(\sqrt{c^2 + d^2}^*\right)}^2} \leadsto \frac{b \cdot c}{{\left(\sqrt{c^2 + d^2}^*\right)}^2} - \frac{d \cdot a}{{\left(\sqrt{c^2 + d^2}^*\right)}^2}\]
8.0
- Taylor expanded around 0 to get
\[\color{red}{\frac{b \cdot c}{{\left(\sqrt{c^2 + d^2}^*\right)}^2}} - \frac{d \cdot a}{{\left(\sqrt{c^2 + d^2}^*\right)}^2} \leadsto \color{blue}{\frac{b \cdot c}{{\left(\sqrt{c^2 + d^2}^*\right)}^2}} - \frac{d \cdot a}{{\left(\sqrt{c^2 + d^2}^*\right)}^2}\]
8.0
- Applied simplify to get
\[\frac{b \cdot c}{{\left(\sqrt{c^2 + d^2}^*\right)}^2} - \frac{d \cdot a}{{\left(\sqrt{c^2 + d^2}^*\right)}^2} \leadsto \frac{b}{\sqrt{c^2 + d^2}^*} \cdot \frac{c}{\sqrt{c^2 + d^2}^*} - \frac{a}{\sqrt{c^2 + d^2}^*} \cdot \frac{d}{\sqrt{c^2 + d^2}^*}\]
0.0
- Applied final simplification
