在三角形ABC中,角A,B,C的对边分别为a,b,c,且满足(2a-c)CosB=bCosC
(1)求角B的大小
(2)设m=(CosA,Cos2A),n=(-12/5,1)且m*n取最小值时,求tan(A-派/4)
人气:261 ℃ 时间:2020-04-11 09:49:02
解答
(1)(2a-c)cosB=bcosC 正弦定理得:(4RsinA-2RsinC)cosB=2RsinBcosC 2sinAcosB=sinBcosC+sinCcosB 2sinAcosB=sin(B+C) 2sinAcosB=sinA 则:cosB=1/2 得B=π/3(2)由于:A+B+C=π,B=π/3则:A属于(0,2π/3)m*n=(cosA,cos...
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