Formules : Différence entre versions
De TravauxIndse
(→Formules d'addition (démonstrations)) |
|||
| Ligne 1 : | Ligne 1 : | ||
====Formules d'addition (démonstrations)==== | ====Formules d'addition (démonstrations)==== | ||
| − | ( | + | # <math> cos(a+b) = cos(a)cos(b) – sin(a)sin(b) </math> |
| + | * <math> cos (a–(-b)) = cos(a)cos(-b) + sin(a)sin(-b) </math> | ||
| + | Or, | ||
| + | * <math> cos(-b) = cos(b) </math> | ||
| + | * <math> sin(-b) = -sin(b) </math> | ||
| + | Donc, | ||
| + | * <math> cos(a+b) = cos(a)cos(b) – sin(a)sin(b) </math> | ||
| − | + | # <math> cos (a-b) = cos(a)cos(b) + sin(a)sin(b) </math> | |
* <math> [cos (a-b)-1]^2 + [sin(a-b)-0]^2 = (cos(b)-cos(a))^2 + (sin(b)-sin(a))^2 </math> | * <math> [cos (a-b)-1]^2 + [sin(a-b)-0]^2 = (cos(b)-cos(a))^2 + (sin(b)-sin(a))^2 </math> | ||
* <math> cos^2(a-b) - 2cos(a-b) + 1 + sin^2(a-b) = cos^2(b) - 2cos(b)cos(a) + cos^2(a)+ sin^2(b) - 2 sin(b)sin(a)+ sin^2(a) </math> | * <math> cos^2(a-b) - 2cos(a-b) + 1 + sin^2(a-b) = cos^2(b) - 2cos(b)cos(a) + cos^2(a)+ sin^2(b) - 2 sin(b)sin(a)+ sin^2(a) </math> | ||
* <math> 2 - 2 cos(a-b) = 2 - 2cos(a)cos(b) - 2sin(a)sin(b) </math> | * <math> 2 - 2 cos(a-b) = 2 - 2cos(a)cos(b) - 2sin(a)sin(b) </math> | ||
* <math> cos(a-b) = cos(a)cos(b) + sin(a)sin(b) </math> | * <math> cos(a-b) = cos(a)cos(b) + sin(a)sin(b) </math> | ||
Version du 20 février 2014 à 09:36
Formules d'addition (démonstrations)
Or,
Donc,
![[cos (a-b)-1]^2 + [sin(a-b)-0]^2 = (cos(b)-cos(a))^2 + (sin(b)-sin(a))^2](/images/math/3/f/6/3f6f4e6442114b788e2d71905990e1f5.png)
