Question

已知向量a=(c0s(2x一兀/3、c0sx十sinx),b=(1,c0sx一sinx),函数f

Answer 1

f(x)=a*b

=cos(2x-π/3)*1+cosx*cosx-sinx*sinx=cos(2x-π/3)+cos2x

=cos2xcosπ/3+sin2xsinπ/3+cos2x

=3/2cos2x+√3sin2x

=√3(√3/2cos2x+1/2sin2x)

=√3sin(2x+π/3)

∵sinx递增区间是[-π/2,π/2]

∴-π/2≤2x+π/3≤π/2 -5π/12≤x≤π/12

∴f(x)递增区间是[-5π/12,π/12]