Initial program 31.5
\[\frac{1 - \cos x}{x \cdot x}\]
- Using strategy
rm Applied flip--31.7
\[\leadsto \frac{\color{blue}{\frac{1 \cdot 1 - \cos x \cdot \cos x}{1 + \cos x}}}{x \cdot x}\]
Applied associate-/l/31.7
\[\leadsto \color{blue}{\frac{1 \cdot 1 - \cos x \cdot \cos x}{\left(x \cdot x\right) \cdot \left(1 + \cos x\right)}}\]
Simplified15.8
\[\leadsto \frac{\color{blue}{\sin x \cdot \sin x}}{\left(x \cdot x\right) \cdot \left(1 + \cos x\right)}\]
Taylor expanded around -inf 15.8
\[\leadsto \color{blue}{\frac{{\left(\sin x\right)}^{2}}{{x}^{2} \cdot \left(\cos x + 1\right)}}\]
Simplified0.3
\[\leadsto \color{blue}{\frac{\frac{\sin x}{x} \cdot \frac{\sin x}{x}}{\cos x + 1}}\]
Final simplification0.3
\[\leadsto \frac{\frac{\sin x}{x} \cdot \frac{\sin x}{x}}{1 + \cos x}\]
