Răspuns:
[tex]sin^2(x+y)-sin^2(x-y)=sin(2x)*sin(2y)[/tex]
Vom demonstra incepand cu partea dreapta a egalitati
[tex]sin(2x)*sin(2y)=2sin(x)*cos(x)*2sin(y)*cos(y)=[/tex]
[tex]=2sin(x)*cos(y)*2sin(y)*cos(x)\\=(sin(x+y)+sin(x-y))*(sin(x+y)-sin(x-y))[/tex]
[tex]=(a+b)(a-b)=a^2-b^2 =>[/tex]
[tex]=sin^2(x+y)-sin^2(x-y)[/tex]
[tex]=> sin^2(x+y)-sin^2(x-y)=sin(2x)*sin(2y)[/tex] "Adevarat"
Formule folosite:
[tex]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)[/tex]
[tex]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)[/tex]
