Initial program 30.6
\[\frac{1 - \cos x}{{x}^2}\]
- Using strategy
rm
Applied flip-- 30.7
\[\leadsto \frac{\color{blue}{\frac{{1}^2 - {\left(\cos x\right)}^2}{1 + \cos x}}}{{x}^2}\]
Applied simplify 14.8
\[\leadsto \frac{\frac{\color{blue}{\sin x \cdot \sin x}}{1 + \cos x}}{{x}^2}\]
- Using strategy
rm
Applied square-mult 14.8
\[\leadsto \frac{\frac{\sin x \cdot \sin x}{1 + \cos x}}{\color{blue}{x \cdot x}}\]
Applied flip3-+ 14.8
\[\leadsto \frac{\frac{\sin x \cdot \sin x}{\color{blue}{\frac{{1}^{3} + {\left(\cos x\right)}^{3}}{{1}^2 + \left({\left(\cos x\right)}^2 - 1 \cdot \cos x\right)}}}}{x \cdot x}\]
Applied associate-/r/ 14.8
\[\leadsto \frac{\color{blue}{\frac{\sin x \cdot \sin x}{{1}^{3} + {\left(\cos x\right)}^{3}} \cdot \left({1}^2 + \left({\left(\cos x\right)}^2 - 1 \cdot \cos x\right)\right)}}{x \cdot x}\]
Applied times-frac 14.7
\[\leadsto \color{blue}{\frac{\frac{\sin x \cdot \sin x}{{1}^{3} + {\left(\cos x\right)}^{3}}}{x} \cdot \frac{{1}^2 + \left({\left(\cos x\right)}^2 - 1 \cdot \cos x\right)}{x}}\]
Applied simplify 0.4
\[\leadsto \color{blue}{\frac{\sin x \cdot \frac{\sin x}{x}}{1 + {\left(\cos x\right)}^3}} \cdot \frac{{1}^2 + \left({\left(\cos x\right)}^2 - 1 \cdot \cos x\right)}{x}\]
Applied simplify 0.4
\[\leadsto \frac{\sin x \cdot \frac{\sin x}{x}}{1 + {\left(\cos x\right)}^3} \cdot \color{blue}{\frac{\cos x \cdot \cos x + \left(1 - \cos x\right)}{x}}\]
Applied simplify 0.4
\[\leadsto \frac{\sin x \cdot \frac{\sin x}{x}}{1 + {\left(\cos x\right)}^3} \cdot \frac{\color{blue}{\left(1 - \cos x\right) + {\left(\cos x\right)}^2}}{x}\]
- Removed slow pow expressions
