已知tanx,tany是方程x^2+6x+7=0的两个根,求证sin(x+y)=cos(x+y).
问题描述:
已知tanx,tany是方程x^2+6x+7=0的两个根,求证sin(x+y)=cos(x+y).
答
tanx+tany=-6,tanx*tany=7
tan(x+y)=(tanx+tany)/(1-tanxtany)
=(-6)/(1-7)=1
tan(x+y)=sin(x+y)/cos(x+y)=1
sin(x+y)=cos(x+y).