向量a=(1,2sinx),向量b=(2cos(x+π/6),1),
函数f(x)=向量a•向量b=2cos(x+π/6)+ 2sinx
=2(cosxcosπ/6-sinxsinπ/6) + 2sinx
=√3cosx-sinx+ 2sinx
=√3cosx+sinx
=2cos(x-π/6)
因为f(x)=8/5,所以cos(x-π/6)=4/5.
∴cos(2x-π/3)=cos[2(x-π/6)]
=2 cos²(x-π/6)-1=7/25.
向量a=(1,2sinx),向量b=(2cos(x+π/6),1),
函数f(x)=向量a•向量b=2cos(x+π/6)+ 2sinx
=2(cosxcosπ/6-sinxsinπ/6) + 2sinx
=√3cosx-sinx+ 2sinx
=√3cosx+sinx
=2cos(x-π/6)
因为f(x)=8/5,所以cos(x-π/6)=4/5.
∴cos(2x-π/3)=cos[2(x-π/6)]
=2 cos²(x-π/6)-1=7/25.