Initial program 31.0
\[\frac{1 - \cos x}{x \cdot x}\]
- Using strategy
rm Applied flip--31.1
\[\leadsto \frac{\color{blue}{\frac{1 \cdot 1 - \cos x \cdot \cos x}{1 + \cos x}}}{x \cdot x}\]
Applied associate-/l/31.2
\[\leadsto \color{blue}{\frac{1 \cdot 1 - \cos x \cdot \cos x}{\left(x \cdot x\right) \cdot \left(1 + \cos x\right)}}\]
Simplified15.3
\[\leadsto \frac{\color{blue}{\sin x \cdot \sin x}}{\left(x \cdot x\right) \cdot \left(1 + \cos x\right)}\]
Taylor expanded around inf 15.3
\[\leadsto \color{blue}{\frac{{\left(\sin x\right)}^{2}}{{x}^{2} \cdot \left(\cos x + 1\right)}}\]
Simplified0.3
\[\leadsto \color{blue}{\frac{\frac{\sin x}{x} \cdot \frac{\sin x}{x}}{\cos x + 1}}\]
- Using strategy
rm Applied add-cube-cbrt0.5
\[\leadsto \frac{\color{blue}{\left(\left(\sqrt[3]{\frac{\sin x}{x}} \cdot \sqrt[3]{\frac{\sin x}{x}}\right) \cdot \sqrt[3]{\frac{\sin x}{x}}\right)} \cdot \frac{\sin x}{x}}{\cos x + 1}\]
Final simplification0.5
\[\leadsto \frac{\frac{\sin x}{x} \cdot \left(\sqrt[3]{\frac{\sin x}{x}} \cdot \left(\sqrt[3]{\frac{\sin x}{x}} \cdot \sqrt[3]{\frac{\sin x}{x}}\right)\right)}{\cos x + 1}\]
