Mathc initiation/a0020
Vérifier quelques propriétés mathématiques de trigonométrie
Vérifions si : sin(x)sin(y) = 1/2 [cos(x-y) - cos(x+y)]
Nous avons vu que :
cos(x-y) = cos(x)cos(y) + sin(x)sin(y)
cos(x+y) = cos(x)cos(y) - sin(x)sin(y)
Donc
cos(x-y) - cos(x+y) = [cos(x)cos(y) + sin(x)sin(y)] - [cos(x)cos(y) - sin(x)sin(y)]
= cos(x)cos(y) + sin(x)sin(y) - cos(x)cos(y) + sin(x)sin(y)
= 2 sin(x)sin(y)
Soit
sin(x)sin(y) = 1/2 [cos(x-y) - cos(x+y)]