隆力奇净水器价格:求证:ctgActgB+ctgBctgC+ctgCctgA=1

来源:百度文库 编辑:高校问答 时间:2024/05/08 05:46:56

0=sin(A+B+C)
=sin(A+B)cosC+cos(A+B)sinC
=(sinAcosB+cosAsinB)cosC+(cosAcosB-sinAsinB)sinC
=sinAcosBcosC+cosAsinBcosC+cosAcosBsinC-sinAsinBsinC

所以sinAsinBsinC=sinAcosBcosC+cosAsinBcosC+cosAcosBsinC
所以(sinAcosBcosC+cosAsinBcosC+cosAcosBsinC)/sinAsinBsinC=1
即ctgActgB+ctgBctgC+ctgCctgA=1