F.4(A MATHS)
2007-03-16 6:08 am
1.Let A,Band C be the interior angles of △ABC. If sinA=2cosBsinC, porve that△ABC is isosceles.
回答 (2)
2007-03-16 6:45 am
✔ 最佳答案
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
2007-03-16 6:49 am
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.
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.
參考: EM
收錄日期: 2021-04-12 23:34:07
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