F.4(A MATHS)

因sinA
=sin[180-(B+C)]
=sin(B+C)
=sinBcosC+cosBsinC
而sinA=2cosBsinC
即sinBcosC+cosBsinC=2cosBsinC
sinBcosC=cosBsinC
sinB/cosB=sinC/cosC
tanB=tanC
因B及C都小於180度
所以B=C
即△ABC is isosceles

2007-03-15 22:46:50 補充：
因B及C都大於0小於180度

1.Let A,Band C be the interior angles of △ABC. If sinA=2cosBsinC, porve that△ABC is isosceles.
A + B + C = 180
sinA = 2cosBsinC
sin[180 - (B + C)] = 2cosBsinC
sinBcosC + sinCcosB = 2cosBsinC
sinBcosC = cosBsinC
sinBcosC - cosBsinC = 0
sin(B - C) = 0
B - C = 0
B = C
△ABC is isosceles.