Question

$frac{tg3a}{tga}= frac{3- tg^{2} a }{1-3 tg^{2}a }$

Answer 1

tg3a/tga=tg(2a+a)/tga=tg2a+tga/1-tg2atga/tga=tg2a+tga/(1-tg2atga)tga)=2tga/1-tg^2a+tga/(1-2tga/1-tg^2a*tga)tga=tga(2/1-tg^2a+1)/(1-2tg^2a/1-tg2^a)tga=2+1-tg^2a/1-tg^2a/1-tg^2a-2tg^2a/1-tg^2a=3-tg^2a/1-3tg^2a.
Тождество доказано.