Initial program 13.5
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
- Using strategy
rm Applied tan-quot13.5
\[\leadsto x + \left(\tan \left(y + z\right) - \color{blue}{\frac{\sin a}{\cos a}}\right)\]
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
\[\leadsto x + \color{blue}{\frac{\left(\tan y + \tan z\right) \cdot \cos a - \left(1 - \tan y \cdot \tan z\right) \cdot \sin a}{\left(1 - \tan y \cdot \tan z\right) \cdot \cos a}}\]
Simplified0.2
\[\leadsto x + \frac{\color{blue}{(\left(\tan y + \tan z\right) \cdot \left(\cos a\right) + \left((\left(\tan y\right) \cdot \left(\tan z\right) + -1)_* \cdot \sin a\right))_*}}{\left(1 - \tan y \cdot \tan z\right) \cdot \cos a}\]
- Using strategy
rm Applied flip3--0.2
\[\leadsto x + \frac{(\left(\tan y + \tan z\right) \cdot \left(\cos a\right) + \left((\left(\tan y\right) \cdot \left(\tan z\right) + -1)_* \cdot \sin a\right))_*}{\color{blue}{\frac{{1}^{3} - {\left(\tan y \cdot \tan z\right)}^{3}}{1 \cdot 1 + \left(\left(\tan y \cdot \tan z\right) \cdot \left(\tan y \cdot \tan z\right) + 1 \cdot \left(\tan y \cdot \tan z\right)\right)}} \cdot \cos a}\]
Applied associate-*l/0.2
\[\leadsto x + \frac{(\left(\tan y + \tan z\right) \cdot \left(\cos a\right) + \left((\left(\tan y\right) \cdot \left(\tan z\right) + -1)_* \cdot \sin a\right))_*}{\color{blue}{\frac{\left({1}^{3} - {\left(\tan y \cdot \tan z\right)}^{3}\right) \cdot \cos a}{1 \cdot 1 + \left(\left(\tan y \cdot \tan z\right) \cdot \left(\tan y \cdot \tan z\right) + 1 \cdot \left(\tan y \cdot \tan z\right)\right)}}}\]
Applied associate-/r/0.2
\[\leadsto x + \color{blue}{\frac{(\left(\tan y + \tan z\right) \cdot \left(\cos a\right) + \left((\left(\tan y\right) \cdot \left(\tan z\right) + -1)_* \cdot \sin a\right))_*}{\left({1}^{3} - {\left(\tan y \cdot \tan z\right)}^{3}\right) \cdot \cos a} \cdot \left(1 \cdot 1 + \left(\left(\tan y \cdot \tan z\right) \cdot \left(\tan y \cdot \tan z\right) + 1 \cdot \left(\tan y \cdot \tan z\right)\right)\right)}\]
Simplified0.2
\[\leadsto x + \frac{(\left(\tan y + \tan z\right) \cdot \left(\cos a\right) + \left((\left(\tan y\right) \cdot \left(\tan z\right) + -1)_* \cdot \sin a\right))_*}{\left({1}^{3} - {\left(\tan y \cdot \tan z\right)}^{3}\right) \cdot \cos a} \cdot \color{blue}{(\left(\tan z \cdot \tan y\right) \cdot \left((\left(\tan y\right) \cdot \left(\tan z\right) + 1)_*\right) + 1)_*}\]
Final simplification0.2
\[\leadsto (\left(\tan z \cdot \tan y\right) \cdot \left((\left(\tan y\right) \cdot \left(\tan z\right) + 1)_*\right) + 1)_* \cdot \frac{(\left(\tan y + \tan z\right) \cdot \left(\cos a\right) + \left((\left(\tan y\right) \cdot \left(\tan z\right) + -1)_* \cdot \sin a\right))_*}{\cos a \cdot \left(1 - {\left(\tan z \cdot \tan y\right)}^{3}\right)} + x\]
