m=(√3sinx/4,1),n=(cosx/4,cos2x/4)
f(x)=m*n=√3sinx/4*cosx/4+cos2x/4
=(√3/2)*2sinx/4*cosx/4+(1/2)(1+cosx/2)
=cos(π/6)sinx/2+sin(π/6)cosx/2+1/2
=sin(x/2+π/6)+1/2
利用正弦定理:a=2RsinA,b=2RsinB,c=2RsinC,代入
(2a-c)cosB=bcosC 得到:
4RsinAcosB-2RsinCcosB=2RsinBcosC
消去2R,移项:
2sinAcosB=sinBcosC+cosBsinC=sin(B+C)=sinA
cosB=1/2,B=π/3 A+C=2π/3
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