先整理化简
f(x)=向量mn-1/2=sinwxcoswx+(coswx)^2-1/2=1/2sin2wx+1/2cos2wx=√2/2sin(2wx+π/4)
最小正周期是4兀 ,最小正周期是4兀 ,w=1/4,f(x)=√2/2sin(1/2x+π/4)
(1)当sin(1/2x+π/4)=-1取得最小值-√2/2,此时1/2x+π/4=-π/2+2kπ,x=-3π/2+4kπ
当sin(1/2x+π/4)=1取得最大值√2/2,,此时1/2x+π/4=π/2+2kπ.x=π/2+4kπ
(2)(2a-c)cosB=bcosC
由正弦定理a/sinA=b/sinB=csinC=2R
则(2sinA-sinC)cosB=sinBcosC
2sinAcosB-sinCcosB=sinBcosC
2sinAcosB=sinCcosB+sinBcosC
2sinAcosB=sin(B+C)
2sinAcosB=sin(180-A)
2sinAcosB=sinA
sinA≠0,所以cosB=1/2,B=π/3
A=2π/3-C,0<A<2π/3,π/4<1/2A+π/4<7π/12,√2/2<sin(1/2A+π/4)≤1
所以1/2<f(A)≤√2/2
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