Update cheatsheet.fr.md

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

@@ -811,7 +811,7 @@ $`\quad\boldsymbol{\mathbf{=\color{brown}{2\,A\cdot cos\Big(\dfrac{\varphi_1-\va
   $`\quad\quad\quad=\sqrt{4\,A^2 \cdot cos^2\Big(\dfrac{\varphi_1 - \varphi_2}{2}\Big)}`$   
   <br>
   $`\color{blue}{\scriptsize{\left.\begin{align} \quad\quad &cos(a+b)=cos(a)cos(b)-sin(a)sin(b)\\
-                     &cos(a-b)=cos(a)cos(b)+-sin(a)sin(b)\end{align}
+                     &cos(a-b)=cos(a)cos(b)+sin(a)sin(b)\end{align}
                \right\}\Longrightarrow\\
         \quad\quad cos^2(a)=cos(a)cos(a)=\dfrac{1}{2}[cos(a+a)+cos(a-a)]\\
         \quad\quad\quad\quad=\dfrac{1}{2}[1 + cos(2a)]}}`$   
@@ -1419,20 +1419,31 @@ $`\quad\quad \;\; = \cdots`$
 <br>
 **$`\quad\quad\;\;=\,\theta_{moy}(\overrightarrow{r},t)\,-\,\theta_{1-2}(\overrightarrow{r},t)`$**  
 
-à terminer,
-
-
-
-
-$`cos\theta_1+cos\theta_2 =`$$`\;\underbrace{cos\,(\theta_{moy}+\Delta\theta_{1-2})+cos\,(\theta_{moy}-\Delta\theta_{1-2}}
-_{\color{blue}{cos(a+b)=cos\,a \,cos\,b\;-\;sin\a\,sin\,b}}`$
 
-$`\quad\;\; = cos\,\theta_{moy}\;cos\,\Delta\theta_{1-2}\;-\;sin\,\theta_{moy}\;sin\,\Delta\theta_{1-2}`$
+* *Travaillons* les **termes $`(cos\theta_1+cos\theta_2)`$ et $`(cos\theta_1-cos\theta_2)`$* qui interviennent
+  dans l'expression de $`U(\vec{r},t)`$ :   
+  <br>
+  **$`cos\theta_1+cos\theta_2 =`$**$`\;cos\,(\theta_{moy}+\Delta\theta_{1-2})+cos\,(\theta_{moy}-\Delta\theta_{1-2}`$   
+  <br>
+  $`\color{blue}{\scriptsize{\left.\begin{align} \quad\quad &cos(a+b)=cos(a)cos(b)-sin(a)sin(b)\\
+                     &cos(a-b)=cos(a)cos(b)+-sin(a)sin(b)\end{align}
+               \right\}\Longrightarrow\\
+        \quad\quad cos(a+b)\,+\,cos(a-b)\,=\,2\,cos(a)\,cos(b)}}`$  
+  <br>
+  **$`\quad\;\; = 2\,cos\,\theta_{moy}\;cos\,\Delta\theta_{1-2}`$**   
+  <br>
+  de même   
+  <br>
+  **$`cos\theta_1-cos\theta_2 =`$**$`\;cos\,(\theta_{moy}+\Delta\theta_{1-2})-cos\,(\theta_{moy}-\Delta\theta_{1-2}`$   
+  <br>
+  $`\color{blue}{\scriptsize{\left.\begin{align} \quad\quad &cos(a+b)=cos(a)cos(b)-sin(a)sin(b)\\
+                     &cos(a-b)=cos(a)cos(b)+-sin(a)sin(b)\end{align}
+               \right\}\Longrightarrow\\
+        \quad\quad cos(a+b)\,-\,cos(a-b)\,=\,-\,2\,sin(a)\,sin(b)}}`$  
+  <br>
+  **$`\quad\;\; = -\,2\,sin\,\theta_{moy}\;sin\,\Delta\theta_{1-2}`$**
 
-de même
 
-$`cos\theta_1-cos\theta_2 =`$$`\;\underbrace{cos\,(\theta_{moy}+\Delta\theta_{1-2})-cos\,(\theta_{moy}-\Delta\theta_{1-2}}
-_{\color{blue}{cos(a-b)=cos\,a \,cos\,b\;+\;sin\a\,sin\,b}}`$