007电影国语在线观看:求证:ctgActgB+ctgBctgC+ctgCctgA=1

来源:百度文库 编辑:查人人中国名人网 时间:2024/04/27 00:04:00

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