Initial program 13.3
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
- Using strategy
rm Applied tan-quot13.3
\[\leadsto x + \left(\tan \left(y + z\right) - \color{blue}{\frac{\sin a}{\cos a}}\right)\]
Applied tan-sum0.2
\[\leadsto x + \left(\color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}} - \frac{\sin a}{\cos a}\right)\]
Applied frac-sub0.2
\[\leadsto x + \color{blue}{\frac{\left(\tan y + \tan z\right) \cdot \cos a - \left(1 - \tan y \cdot \tan z\right) \cdot \sin a}{\left(1 - \tan y \cdot \tan z\right) \cdot \cos a}}\]
- Using strategy
rm Applied flip3--0.2
\[\leadsto x + \frac{\left(\tan y + \tan z\right) \cdot \cos a - \left(1 - \tan y \cdot \tan z\right) \cdot \sin a}{\color{blue}{\frac{{1}^{3} - {\left(\tan y \cdot \tan z\right)}^{3}}{1 \cdot 1 + \left(\left(\tan y \cdot \tan z\right) \cdot \left(\tan y \cdot \tan z\right) + 1 \cdot \left(\tan y \cdot \tan z\right)\right)}} \cdot \cos a}\]
Applied associate-*l/0.2
\[\leadsto x + \frac{\left(\tan y + \tan z\right) \cdot \cos a - \left(1 - \tan y \cdot \tan z\right) \cdot \sin a}{\color{blue}{\frac{\left({1}^{3} - {\left(\tan y \cdot \tan z\right)}^{3}\right) \cdot \cos a}{1 \cdot 1 + \left(\left(\tan y \cdot \tan z\right) \cdot \left(\tan y \cdot \tan z\right) + 1 \cdot \left(\tan y \cdot \tan z\right)\right)}}}\]
Applied associate-/r/0.2
\[\leadsto x + \color{blue}{\frac{\left(\tan y + \tan z\right) \cdot \cos a - \left(1 - \tan y \cdot \tan z\right) \cdot \sin a}{\left({1}^{3} - {\left(\tan y \cdot \tan z\right)}^{3}\right) \cdot \cos a} \cdot \left(1 \cdot 1 + \left(\left(\tan y \cdot \tan z\right) \cdot \left(\tan y \cdot \tan z\right) + 1 \cdot \left(\tan y \cdot \tan z\right)\right)\right)}\]
Simplified0.2
\[\leadsto x + \frac{\left(\tan y + \tan z\right) \cdot \cos a - \left(1 - \tan y \cdot \tan z\right) \cdot \sin a}{\left({1}^{3} - {\left(\tan y \cdot \tan z\right)}^{3}\right) \cdot \cos a} \cdot \color{blue}{\left(\left(1 + \tan z \cdot \tan y\right) + \left(\tan z \cdot \tan y\right) \cdot \left(\tan z \cdot \tan y\right)\right)}\]
- Using strategy
rm Applied add-exp-log0.2
\[\leadsto x + \frac{\left(\tan y + \tan z\right) \cdot \cos a - \left(1 - \tan y \cdot \tan z\right) \cdot \sin a}{\left({1}^{3} - {\left(\tan y \cdot \tan z\right)}^{3}\right) \cdot \cos a} \cdot \left(\left(1 + \tan z \cdot \tan y\right) + \color{blue}{e^{\log \left(\left(\tan z \cdot \tan y\right) \cdot \left(\tan z \cdot \tan y\right)\right)}}\right)\]
Final simplification0.2
\[\leadsto \left(e^{\log \left(\left(\tan z \cdot \tan y\right) \cdot \left(\tan z \cdot \tan y\right)\right)} + \left(1 + \tan z \cdot \tan y\right)\right) \cdot \frac{\cos a \cdot \left(\tan y + \tan z\right) - \left(1 - \tan z \cdot \tan y\right) \cdot \sin a}{\cos a \cdot \left(1 - {\left(\tan z \cdot \tan y\right)}^{3}\right)} + x\]
