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Mathc initiation/Fichiers c : c78ha2

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Sommaire


Installer et compiler ces fichiers dans votre répertoire de travail.

c01a.c
/* --------------------------------- */
/* save as c1a.c                     */
/* --------------------------------- */
#include "x_hfile.h"
#include      "fa.h"
/* --------------------------------- */
int main(void)
{
double x  = 1.2;
double y  = 1.5;

 clrscrn();
 
 printf("  (x,y) = (%0.1f,%0.1f)   \n\n\n",x,y);
 
 
 printf("  %s \t\t\t= %0.8f\n", f1eq, f1(x,y));
 printf("  %s \t= %0.8f  \n\n\n", f2eq, f2(x,y));

 stop();

 return 0;
}
/* ---------------------------------- */
/* ---------------------------------- */


Vérifions par le calcul :
  (x,y) = (1.2,1.5)   


  sinh(x) + sinh(y) 			    = 3.63874081
  2 sinh((x+y)/2)  cosh((x-y)/2) 	= 3.63874081  


 Press return to continue.


Vérifions les égalités : 
     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)