已知向量m=(根号3sinx/4,1),向量n=(cosx/4,cos^2 x/4) ,函数f〔x〕=mn.若f〔x〕=
3个回答

1.m·n=√3sin(x/4)cos(x/4)+cos²(x/4)

=(√3/2)sin(x/2)+(1/2)cos(x/2)+1/2

=cos(x/2-π/3)+1/2=1

cos(x/2-π/3)=-1/2.x/2-π/3=±2π/3+2kπ,x/2= ±2π/3+2kπ+ π/3

x=±4π/3+4kπ+ 2π/3,x+π/3=±4π/3+4kπ+ π

cos(∏/3+x)=1/2

2,f(A)=cos(∠A/2-π/3)+1/2

(2a-c)cosB=bcosC,从正弦定理,(2sinA+sinC)cosB=sinBcosC

可得sinA(2cosB-1)=0 sinA≠0,2cosB-1=0.∠B=π/3

0<∠A<2π/3.-π/3<[∠A/2-π/3]<0.-1/2<cos[∠A/2-π/3]<0

0<f(A)<1/2.