tanA＋tanB＋tanC-(tanAtanBtanC)=0
両辺にcosAcosBcosCをかけると、
sin(A)cos(B)cos(C)+cos(A)sin(B)cos(C)+cos(A)cos(B)sin(C)-sin(A)sin(B)sin(C)
={sin(A)cos(B)+cos(A)sin(B)}cos(C)+{cos(A)cos(B)-sin(A)sin(B)}sin(C)
=sin(A+B)cos(C)+cos(A+B)sin(C)=sin((A+B)+C)=sin(180)=0