Răspuns:
Aplici formula tg(a+b)=(ta+tgb)/1-tga*tgb)
tg75=tg(30+45)=(tg30+tg45)/(1-tg30*tg45)=(√3/3+1)/(1-√3/3)=
[(√3+3)/3](3-√3)/3=(3+√3)/(3-√3)
tg15=tg(45-30)=(tg45-tg30)/(1+tg45*tg30)=
(1-√3/3)/(1+1*√3/3)=(3-√3)/(3+√3)
tg75-tg15=
(3+√3)/(3-√3)-(3-√3)/(3+√3)=
[(3+√3)²-(3-√3)²]/(3²-√3²)=
(9+6√3+3-9+6√3-3)/(9-3)=
6√3/6=√3
Explicație pas cu pas:
