Initial program 0.0
\[\Re(\left(\frac{e^{x} + e^{-x}}{2} \cdot \cos y + \frac{e^{x} - e^{-x}}{2} \cdot \sin y i\right))\]
Simplified0.0
\[\leadsto \color{blue}{\frac{(\left(\cos y\right) \cdot \left(e^{x}\right) + \left(\frac{\cos y}{e^{x}}\right))_*}{2}}\]
- Using strategy
rm Applied add-sqr-sqrt0.0
\[\leadsto \frac{(\left(\cos y\right) \cdot \left(e^{x}\right) + \left(\frac{\cos y}{\color{blue}{\sqrt{e^{x}} \cdot \sqrt{e^{x}}}}\right))_*}{2}\]
Applied associate-/r*0.0
\[\leadsto \frac{(\left(\cos y\right) \cdot \left(e^{x}\right) + \color{blue}{\left(\frac{\frac{\cos y}{\sqrt{e^{x}}}}{\sqrt{e^{x}}}\right)})_*}{2}\]
- Using strategy
rm Applied *-un-lft-identity0.0
\[\leadsto \frac{(\left(\cos y\right) \cdot \left(e^{x}\right) + \left(\frac{\frac{\cos y}{\sqrt{e^{x}}}}{\sqrt{e^{\color{blue}{1 \cdot x}}}}\right))_*}{2}\]
Applied exp-prod0.0
\[\leadsto \frac{(\left(\cos y\right) \cdot \left(e^{x}\right) + \left(\frac{\frac{\cos y}{\sqrt{e^{x}}}}{\sqrt{\color{blue}{{\left(e^{1}\right)}^{x}}}}\right))_*}{2}\]
Applied sqrt-pow10.0
\[\leadsto \frac{(\left(\cos y\right) \cdot \left(e^{x}\right) + \left(\frac{\frac{\cos y}{\sqrt{e^{x}}}}{\color{blue}{{\left(e^{1}\right)}^{\left(\frac{x}{2}\right)}}}\right))_*}{2}\]
Simplified0.0
\[\leadsto \frac{(\left(\cos y\right) \cdot \left(e^{x}\right) + \left(\frac{\frac{\cos y}{\sqrt{e^{x}}}}{{\color{blue}{e}}^{\left(\frac{x}{2}\right)}}\right))_*}{2}\]
Final simplification0.0
\[\leadsto \frac{(\left(\cos y\right) \cdot \left(e^{x}\right) + \left(\frac{\frac{\cos y}{\sqrt{e^{x}}}}{{e}^{\left(\frac{x}{2}\right)}}\right))_*}{2}\]
