Question

решите систему уравнений: tg(x-y)=-1/2 2tg x +tg y=5 ( все это в фигурной скобке)

Answer 1

2*tgy=5 -> tgy=5/2

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

(tgx-5/2)/(1+tgx*5/2)=-1/2

tgx-5/2=(-1/2)*(1+tgx*5/2)

tgx=(-1/2)-tgx*(5/4)

tgx+(5/4)*tgx=-1/2

(9/4)tgx=-1/2

tgx=(-1/2)/(9/4)

tgx=-2/9

 

 

Answer 2

2*tgy=5 -> tgy=5/2 tg(x-y)=(tgx-tgy)/(1+tgx*tgy) (tgx-5/2)/(1+tgx*5/2)=-1/2 tgx-5/2=(-1/2)*(1+tgx*5/2)  tgx=(-1/2)-tgx*(5/4)  tgx+(5/4)*tgx=-1/2 (9/4)tgx=-1/2 tgx=(-1/2)/(9/4) tgx=-2/9.