Question

Qual o valor da tg x, se a tg(x+y)=22 e a tg y= 4/9?

Answer 1

$Ola' \\ \\ tg(x+y)=22~~~--\ \textgreater \ Se~sabe~que:\begin{cases}tgy= \frac{4}{9} \\ \\ tgx=? \end{cases} \\ \\ Enta\~ao: \\ \\ \underbrace{tg(x+y)}=22 \\ \frac{tgx+tgy}{1-tgx.tgy} =22 \\ \\ \frac{tgx+ \frac{4}{9} }{1-tgx.( \frac{4}{9}) } =22~~--\ \textgreater \ desenvolvendo~temos: \\ \\ 9tgx+4=198-88tgx~~--\ \textgreater \ isolando~(tgx) \\ \\ 9tgx+88tgx=198-4 \\ \\ 97tgx=192 \\ \\ \boxed{\boxed{tgx=2}}~~--\ \textgreater \ resposta \\ \\ \\ \mathbb{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Espero~ter~ajudado!!$