Question

Dados tg x = t e tg y= t/2 , determine tg(x-y) em função t.

Answer 1

$tg(x-y)=\frac{tg(x)-tg(y)}{1+tg(x).tg(y)}=\frac{t-\frac{t}{2}}{1+t.\frac{t}{2}}=\frac{\frac{t}{2}}{1+\frac{t^2}{2}}=\frac{\frac{t}{2}}{\frac{t^2+2}{2}}=\boxed{\frac{t}{t^2+2}}$