11.在△ABC中,求证sinA+sinB+sinC=4cos(A/2)cos(B/2)cos(C/2)_数学解答

11.在△ABC中,求证sinA+sinB+sinC=4cos(A/2)cos(B/2)cos(C/2)

人气：370 ℃　时间：2019-12-08 00:47:54

解答

证明： ∵在三角形ABC中, ∴A+B+C=180度,得SINA=SIN（B+C）则A/2=90度-（B+C）/2,得COSA/2=SIN（（B+C）/2）左边=Sin(B+C)+SinB+SinC 则4Cos(A/2)Cos(B/2)Cos(C/2) =4Sin((B+C)/2)Cos(B/2)Cos(C/2) =4Cos(B/2)Cos(...