Verified answer

1-2·cosx + cos(2x)= 1- 2·cosx+ cos²x- sen²x = (1-sen²x) - 2·cosx + cos²x= cos²x-2·cosx + cos²x =

2·cos²x-2·cosx = 2·cosx· (cosx-1) = -2·cosx· (1-cosx)

lim{x-->0} F(x)= lim{x-->0} -2· cosx · (1-cosx)/x²= -2·cos0 ·lim{x-->0} (1-cosx)/x² ·(1+cosx)/(1+cosx) =

-2·cos0/(1+cos0) ·lim{x-->0} (1-cos²x)/x² = -2/2 ·lim{x-->0} sen²x/x² = -1· [lim{x-->0} senx/x]² = -1·1 = -1

Saludos