Initial program 37.4
\[\sin \left(x + \varepsilon\right) - \sin x\]
Initial simplification37.4
\[\leadsto \sin \left(\varepsilon + x\right) - \sin x\]
- Using strategy
rm Applied sin-sum22.1
\[\leadsto \color{blue}{\left(\sin \varepsilon \cdot \cos x + \cos \varepsilon \cdot \sin x\right)} - \sin x\]
Applied associate--l+0.4
\[\leadsto \color{blue}{\sin \varepsilon \cdot \cos x + \left(\cos \varepsilon \cdot \sin x - \sin x\right)}\]
- Using strategy
rm Applied *-un-lft-identity0.4
\[\leadsto \sin \varepsilon \cdot \cos x + \left(\cos \varepsilon \cdot \sin x - \color{blue}{1 \cdot \sin x}\right)\]
Applied distribute-rgt-out--0.4
\[\leadsto \sin \varepsilon \cdot \cos x + \color{blue}{\sin x \cdot \left(\cos \varepsilon - 1\right)}\]
Taylor expanded around -inf 22.1
\[\leadsto \color{blue}{\left(\cos x \cdot \sin \varepsilon + \sin x \cdot \cos \varepsilon\right) - \sin x}\]
Simplified0.4
\[\leadsto \color{blue}{(\left(\cos x\right) \cdot \left(\sin \varepsilon\right) + \left(\sin x \cdot \cos \varepsilon - \sin x\right))_*}\]
- Using strategy
rm Applied fma-neg0.4
\[\leadsto (\left(\cos x\right) \cdot \left(\sin \varepsilon\right) + \color{blue}{\left((\left(\sin x\right) \cdot \left(\cos \varepsilon\right) + \left(-\sin x\right))_*\right)})_*\]
Final simplification0.4
\[\leadsto (\left(\cos x\right) \cdot \left(\sin \varepsilon\right) + \left((\left(\sin x\right) \cdot \left(\cos \varepsilon\right) + \left(-\sin x\right))_*\right))_*\]
