Răspuns:
Am inlocuit Alfa cu x si Beta cu y
[tex]\frac{sin^2(x+y)+sin^2(x-y)}{2cos^2x*cos^2y}=tg^2x+tg^2y[/tex]
[tex]\frac{(sinx*cosy+siny*cosx)^2+(sinx*cosy-siny*cosx^2)}{2cos^2x*cos^2y}=tg^2x+tg^2y[/tex]
[tex]\frac{sin^2x*cos^2y+sin^2y*cos^2x+2sinx*cosy*siny*cosx+sin^2x*cos^2y+sin^2y*cos^2x-2sinx*cosy*siny*cosx}{2cos^2x*cos^2y}[/tex]
[tex]\frac{2sin^2x*cos^2y+2sin^2y*cos^2x}{2cos^2x*cos^2y}=tg^2x+tg^2y[/tex]
[tex]\frac{2(sin^2x*cos&^2y+sin^2y*cos^2x)}{2cos^2x*cos^2y}=tg^2x+tg^2y[/tex]
[tex]\frac{sin^2x*cos^2y+sin^2y*cos^2x}{cos^2x*cos^2y}=tg^2x+tg^2y[/tex]
[tex]tg^2x+tg^2y=tg^2x+tg^2y[/tex] "Adevarat"
