Mathc initiation/a00z
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)
cos(x)sin(y)+sin(x)cos(y)
= -------------------------
cos(x)cos(y)-sin(x)sin(y)
cos(x)sin(y)+sin(x)cos(y) (1/(cos(x)cos(y))
= -------------------------
cos(x)cos(y)-sin(x)sin(y) (1/(cos(x)cos(y))
cos(x)sin(y) sin(x)cos(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(y) + tan(x)
= -----------------------------
1 - tan(x)tan(y)
soit
tan(x) + tan(y)
tan(x+y) = ----------------
1 - tan(x)tan(y)