Question

Se tg(x+y)=1 e tgx+tgy=2, calcule tgx*tgy? 

Answer 1

Oi, tudo bem?

$tg(x+y)=1\\ tgx+tgy=2\\ \\ tg(x+y)=\frac { tgx+tgy }{ 1-tgx*tgy } \\ \\ 1=\frac { 2 }{ 1-tgx*tgy } \\ \\ 1(1-tgx*tgy)=2\\ \\ 1-tgx*tgy=2\quad \\ -tgx*tgy=2-1\\ -tgx*tgy=1\quad (-1)\\ tgx*tgy=-1$