Mathc initiation/a0065

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