Question

SE tan(x+y) +2x=5-2y e tan (y-x) +y=7-x, ent o valor de x+y é?

Answer 1

Para resolver temos que:

$tg(- \alpha ) = \dfrac{sen(- \alpha )}{cos(- \alpha )} = \dfrac{-sen( \alpha )}{cos( \alpha )} = -tg( \alpha )$

Logo:

$tg(y-x) = tg[-(x-y)] = -tg(x-y)$

Assim:

$\left \{ {{tg(x+y) + 2x=5-2y} \atop {tg(y-x) +y=7-x}} \right. = \left \{ {{tg(x+y) + 2x=5-2y} \atop {-tg(x-y) +y=7-x}} \right.$

Somando as equações:

$2x + y = 5-2y + 7 - x \\ \\ 3x = 3y = 12 \\ \\ x + y = 4$