Question

Sabendo que Tg(x-y)=-1/3 e que Tgx=2tgy,determine tg x e tg y.

Answer 1

Resposta:

tg(x-y)=(tg(x)-tg(y))/(1+tg(x)*tg(y))

tg(x-y)==-1/3

(tg(x)-tg(y))/(1+tg(x)*tg(y))=-1/3

3*(tg(x)-tg(y))=-1*(1+tg(x)*tg(y))

3t(x)-3tg(y)=-1 -tg(x)*tg(y)

sabemos que tg(x)=2*tg(y)

3*2*tg(y)-3tg(y)=-1 -2*tg(y)*tg(y)

3tg(y)=-1 -2*tg²(y)

2*tg²(y)+3tg(y)+1=0

fazendo tg(y)=z

2z²+3z+1=0

z'=[-3+√(9-8)]/4=(-2+1)/4=-1/4

z''=[-3-√(9-8)]/4=(-2-1)/4=-3/4

z=-1/4=tg(y)  ==>tgx=2tgy==> tg(x)=-1/2=

z=-3/4=tg(y) ==>tgx=2tgy==> tg(x)=-3/2