Question

已知tanx+tany=5m,tan(x+y)=6m(m≠0）,tan（x-y)=1/7,求m的值及tanx,tany的

Answer 1

tan(x+y)=(tanx+tany)/(1-tanxtany)=6m

tanx+tany=5m代入上式

tanxtany=1/6

tan(x-y)=(tanx-tany)/(1+tanxtany)=1/7

tanx-tany=1/6

tanx=1/2,tany=1/3,或tanx=-1/3,tany=-1/2

tanx=1/2,tany=1/3时,m=1/6

tanx=-1/3,tany=-1/2时m=-1/6