Question

Найти tgα, если tg(α-π/4) = 3/4

Answer 1

 

$tgfrac{pi}{4}=1\tg(alpha-beta)=frac{tgalpha-tgbeta}{1+tgalpha*tgbeta}\\\tg(alpha-frac{pi}{4})=frac{tgalpha-tgfrac{pi}{4}}{1+tgalpha*tgfrac{pi}{4}}\frac{3}{4}=frac{tgalpha-1}{1+tgalpha}\3(1+tgalpha)=4(tgalpha-1)\3-3tgalpha=4tgalpha-4\7tgalpha=7\tgalpha=1$