Question

trigonometrie punctul f)​

Answer 1

Răspuns:

$sin^2(x+y)-sin^2(x-y)=sin(2x)*sin(2y)$

Vom demonstra incepand cu partea dreapta a egalitati

$sin(2x)*sin(2y)=2sin(x)*cos(x)*2sin(y)*cos(y)=$

$=2sin(x)*cos(y)*2sin(y)*cos(x)\\=(sin(x+y)+sin(x-y))*(sin(x+y)-sin(x-y))$

$=(a+b)(a-b)=a^2-b^2 =>$

$=sin^2(x+y)-sin^2(x-y)$

$=> sin^2(x+y)-sin^2(x-y)=sin(2x)*sin(2y)$ "Adevarat"

Formule folosite:

$1)sin(x+y)-sin(x-y)=sin(x)*cos(y)+sin(y)*cos(x)-sin(x)*cos(y)+sin(y)*cos(x)=2sin(y)*cos(x)$

$2)sin(x+y)+sin(x-y)=sin(x)*cos(y)+sin(y)*cos(x)+sin(x)*cos(y)-sin(y)*cos(x)=2sin(x)*cos(y)$