Mathc initiation/a0066

Vérifier quelques propriétés mathématiques de trigonométrie hyperbolique

Vérifions si : sinh(x) - sinh(y) = 2 sinh( (x-y)/2 ) cosh( (x+y)/2 )

     sinh(x) - sinh(y) = 2 cosh( (x+y)/2 ) sinh( (x-y)/2 )    
     

                                                         sinh(   X  )  =  [e**X         - e**(-X)      ] / 2
                                                         sinh((x-y)/2) =  [e**((x-y)/2) - e**(-(x-y)/2)] / 2      
                                                         
                                                         cosh(   X  )  =  [e**X         + e**(-X)      ] / 2
                                                         cosh((x+y)/2) =  [e**((x+y)/2) + e**(-(x+y)/2)] / 2

                                                         
     
     sinh(x) - sinh(y)  = 2       cosh( (x+y)/2 )                 sinh( (x-y)/2 )    
     
     sinh(x) - sinh(y)  = 2 [e**((x+y)/2) + e**(-(x+y)/2)]/2   [e**((x-y)/2) - e**(-(x-y)/2)]/2
     
   2[sinh(x) - sinh(y)] =   [e**((x+y)/2) + e**(-(x+y)/2)]     [e**((x-y)/2) - e**(-(x-y)/2)] 
          
      
  
                                                         
                                                         (x+y)/2  +   (x-y)/2   =  x
                                                         (x+y)/2  + (-(x-y)/2)) =  y
                                                        -(x+y)/2) +   (x-y)/2   = -y
                                                        -(x+y)/2) + (-(x-y)/2)  = -x
                                                        
  
  2[sinh(x) - sinh(y)] =    e**x-e**y+e**(-y)-e**(-x)      
     
  2[sinh(x) - sinh(y)] =    e**x-e**(-x)    -  e**y+e**(-y) 
  
  2[sinh(x) - sinh(y)] =    e**x-e**(-x)    - [e**y-e**(-y)]
       
    sinh(x) - sinh(y)  =   [e**x-e**(-x)]/2 - [e**y-e**(-y)]/2    
    
    sinh(x) - sinh(y)  =      sinh(x)       -    sinh(y)