Mathc initiation/a001

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