Question

a-alfa,b-beta

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Вычислите tg (a+b) u tg(a-b), если tga=1/3, tgb=1/5.

Answer 1

$tg(alpha+beta)=frac{tgalpha+tgbeta}{1-tgalpha*tgbeta}=frac{frac{1}{3}+frac{1}{5}}{1-frac{1}{3}*frac{1}{5}}=frac{frac{8}{15}}{frac{14}{15}}=frac{8}{14}=frac{4}{7}\\\tg(alpha-beta)=frac{tgalpha-tgbeta}{1+tgalpha*tgbeta}=frac{frac{1}{3}-frac{1}{5}}{1+frac{1}{3}*frac{1}{5}}=frac{frac{2}{15}}{frac{16}{15}}=frac{2}{16}=frac{1}{8}$