Mathc initiation/a0022

Vérifier quelques propriétés mathématiques de trigonométrie

Vérifions si : sin(x)cos(y) = 1/2 [sin(x-y) + sin(x+y)] 

     Nous avons vu que :
    
    sin(x-y) = sin(x)cos(y) - cos(x)sin(y)
    sin(x+y) = cos(x)sin(y) + sin(x)cos(y)       
    
    Donc 
    
    sin(x-y) + sin(x+y)  = [sin(x)cos(y) - cos(x)sin(y)] + [cos(x)sin(y) + sin(x)cos(y)]
    
                         =  sin(x)cos(y) - cos(x)sin(y)  +  cos(x)sin(y) + sin(x)cos(y)
    
                         =  2 sin(x)cos(y)   
                                                 
    Soit                        
         
          sin(x)cos(y)  =   1/2 [sin(x-y) + sin(x+y)]