Mathc initiation/a00z

Vérifier quelques propriétés mathématiques de trigonométrie

                           tan(x) + tan(y) 
Vérifions si : tan(x+y)  = ----------------   
                           1 - tan(x)tan(y) 

    Nous avons vu que :
    
    
                sin(x+y)    
    tan(x+y) =  --------
                cos(x+y)    
    
                            cos(x)sin(y)+sin(x)cos(y)   
                         =  -------------------------  
                            cos(x)cos(y)-sin(x)sin(y)   


                            cos(x)sin(y)+sin(x)cos(y)  (1/(cos(x)cos(y))
                         =  -------------------------  
                            cos(x)cos(y)-sin(x)sin(y)  (1/(cos(x)cos(y))

    
                            cos(x)sin(y)     sin(x)cos(y) 
                            ------------  +  ------------
                            cos(x)cos(y)     cos(x)cos(y)
                         =  -----------------------------  
                            cos(x)cos(y)     sin(x)sin(y)  
                            ------------  -  ------------
                            cos(x)cos(y)     cos(x)cos(y)
                            
                            
                             tan(y)       +   tan(x)
                          =  -----------------------------     
                             1            -   tan(x)tan(y)
    
    soit
    
                             tan(x) + tan(y)
                 tan(x+y)  = ----------------   
                             1 - tan(x)tan(y)