Update cheatsheet.fr.md

12.temporary_ins/69.waves/30.n3/20.overview/cheatsheet.fr.md

@@ -870,28 +870,29 @@ $`\quad\boldsymbol{\mathbf{=\color{brown}{2\,A\cdot cos\Big(\dfrac{\varphi_1-\va
   $`\cdot\big(\,e^{\,i\varphi_1}\,+\,e^{\,i\varphi_1}\big)`$   
   <br>
   $`\quad =A\;e^{\,i\;(\omega t\,-\, kx)}`$
-  $`\cdot\left(\,e^{\,i\left(\frac{\varphi1 + \varphi2}{2}\;+\;\frac{\varphi1-\varphi2}{2}\right)}`$
-  $`\,+\,e^{\,i\;\left(\frac{\varphi1 + \varphi2}{2}\;-\;\frac{\varphi1-\varphi2}{2}\right)}\right)`$   
+  $`\cdot\Big(\,e^{\,i\big(\frac{\varphi1 + \varphi2}{2}\;+\;\frac{\varphi1-\varphi2}{2}\big)}`$
+  $`\,+\,e^{\,i\;\left(\frac{\varphi1 + \varphi2}{2}\;-\;\frac{\varphi1-\varphi2}{2}\big)}\Big)`$   
    <br>
    $`\color{blue}{\scriptsize{\quad \text{utilisons } exp\,(a+b)\;=\; exp\,(a)\;+\; exp\,(b)}}`$  
    $`\color{blue}{\scriptsize{\quad\text{et regroupons encore les termes communs.}}}`$   
    <br>
    $`\quad = A\;e^{\,i\,(\omega t\,-\, kx)}\,e^{\,i\,\left(\frac{\varphi1 + \varphi2}{2}\right)}`$
-   $`\cdot\left(
-\,e^{\,i\Big(\frac{\varphi1-\varphi2}{2}\Big)}
+   $`\cdot\Big(
+\,e^{\,i\big(\frac{\varphi1-\varphi2}{2}\big)}
 \,+\,
-e^{\,-\,i\;\Big(\frac{\varphi1-\varphi2}{2}\Big)}
-\right)`$
+e^{\,-\,i\;\big(\frac{\varphi1-\varphi2}{2}\big)}
+\Big)`$
    <br>
    $`\color{blue}{\scriptsize{\quad \text{utilisons} \quad exp\,(i\,a)\,+\,exp\,(-\,i\,a)\;=\;2\,cos\,a}}`$  
    <br>
-   $`\quad = A\;e^{\,i\;(\omega t\,-\, kx)}\,e^{\,i\left(\frac{\varphi1 + \varphi2}{2}\right)}`$
+   $`\quad = A\;e^{\,i\;(\omega t\,-\, kx)}\,e^{\,i\,\left(\frac{\varphi1 + \varphi2}{2}\right)}`$
    $`\cdot cos\left(\frac{\varphi1-\varphi2}{2}\right)`$   
   <br>
    $`\quad = A\;cos\left(\frac{\varphi1-\varphi2}{2}\right)\;e^{\,i\,\left(\omega t\,-\, kx\,+\,\frac{\varphi1 + \varphi2}{2}\right)}`$   
    <br>
   L'onde réelle est donc :  
   <br>
+ **$`\mathbf{\underline{U}(x,t)}`$**   
   $`\quad\boldsymbol{\mathbf{=\color{brown}{2\,A\cdot cos\Big(\dfrac{\varphi_1-\varphi_2}{2}\Big) \cdot cos\Big(}\color{blue}{\underbrace{\color{brown}{\omega t - kx + \dfrac{\varphi_1+\varphi_2}{2}}}_{\text{pulsation }\omega\text{ inchangée}}}\color{brown}{\Big)}}}`$
 
   <br>