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