Question

Даю 20Балов!!!
tg(4а)=?, если tg=1/6
по формуле tg(2a)=2tg(a)/(1-tg^2(a))

Answer 1

$tga= frac{1}{6}\\tg2a=frac{2cdot tga}{1-tg^2a} = frac{2cdot frac{1}{6}}{1-frac{1}{36}} = frac{36}{3cdot 35} = frac{12}{35} \\tg4a= frac{2cdot tg2a}{1-tg^22a} = frac{2cdot frac{12}{35}}{1- frac{144}{1225} } = frac{1225cdot 24}{35cdot 1081} = frac{35cdot 24}{1081} = frac{840}{1081}$