已知函数f(x)＝根号3×sin(x/4)cos(x/4)＋(cosx/4)＾2

f(x)＝根号3×sin(x/4)cos(x/4)＋(cosx/4)＾2
＝根号3／2＊sinx/2+(cosx/2+1)/2
＝sinx/2cosPai/6+sinPai/6cosx/2+1/2
=sin(x/2+Pai/6)+1/2
f(x)=1,即有sin(x/2+Pai/6)=1/2
即有cos(Pai/2-x/2-Pai/6)=cos(Pai/3-x/2)=1/2
cos(2Pai/3-x)=2[cos(Pai/3-x/2)]^2-1=2*1/4-1=-1/2
(2)acosC+1/2c=b
acosC＋1/2c=b,则2sinAcosC＋sinC=2sinB=2sin(A＋C)=2sinAcosC＋2cosAsinC,所以sinC=2cosAsinC,得cosA=1/2,A=60°
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