Update cheatsheet.fr.md

12.temporary_ins/07.geometry-coordinates-prop2/40.n4/20.overview/cheatsheet.fr.md

@@ -51,7 +51,9 @@ $`v^2=v\cdot\dfrac{\sin(\theta + \alpha)}{\cos(a)}`$
 $`u_1\,v^1\,+\, u_2\,v^2\,=u\cdot\cos(\alpha)\cdot v\cdot\dfrac{\cos(a + \theta + \alpha)}
 {\cos(a)} + u\cdot\sin(a + \alpha) \cdot v\cdot\dfrac{\sin(\theta + \alpha)}{\cos(a)}`$
 
-$`\quad= u\,v\,\dfrac{1}{\cos(a)} \,[cos(\alpha)\,\cos(a + \theta + \alpha)\,+\,\sin(a + \alpha)\,\sin(\theta + \alpha)]`$
+$`\quad= u\,v\,\dfrac{1}{\cos(a)} \,[\cos(\alpha)\,\cos(a + \theta + \alpha)\,+\,\sin(a + \alpha)\,\sin(\theta + \alpha)]`$
+
+On a
 
 $`\cos(a + \theta + \alpha)=\cos[a + (\theta + \alpha)]=\cos(a)\,\cos(\theta + \alpha)-\sin(a)\,\sin(\theta + \alpha)`$
 
@@ -59,6 +61,33 @@ $`\sin(a + \alpha)=\sin(a)\cos(\alpha)+\sin(\alpha)\cos(a)`$
 
 $`\sin(\theta + \alpha)=\sin(\theta)\cos(\alpha)+\sin(\alpha)\cos(\theta)`$
 
+donc
+
+$`\quad= u\,v\,\dfrac{1}{\cos(a)} \,[\cos(a)\cos(\alpha)\cos(\theta + \alpha)\,-\,\sin(a)\sin(\alpha)\sin(\theta + \alpha)
+\,+\,\sin(a)\,\cos^2(\alpha)\,\sin(\theta)
+\,+\,\sin(a)\,\cos(\alpha)\,\sin(\alpha)\,\cos(\theta)
+\,+\,\cos(a)\,\sin(\alpha)\,\cos(\alpha)\,\sin(\theta)
+\,+\,\cos(a)\,\sin^2(\alpha)\,\cos(\theta)]`$
+
+On a 
+
+$`\cos(\theta + \alpha)=\cos(\theta)\,\cos(\alpha)\,-\,\sin(\theta)\,\sin(\alpha)`$
+
+$`\sin(\theta + \alpha)=\sin(\theta)\,\cos(\alpha)\,+\,\sin(\alpha)\,\cos(\theta)`$
+
+donc
+
+$`\quad= u\,v\,\dfrac{1}{\cos(a)} \,[\cos(a)\cos(\alpha)\cos(\theta + \alpha)\,-\,\sin(a)\sin(\alpha)\sin(\theta + \alpha)
+\,+\,\sin(a)\,\cos^2(\alpha)\,\sin(\theta)
+\,+\,\sin(a)\,\cos(\alpha)\,\sin(\alpha)\,\cos(\theta)
+\,+\,\cos(a)\,\sin(\alpha)\,\cos(\alpha)\,\sin(\theta)
+\,+\,\cos(a)\,\sin^2(\alpha)\,\cos(\theta)]`$
+
+
+
+
+
+