Question

已知cos(π/6-α)=根号3/3,则sin^2=(α-π/6)-cos(5π/6+α)的值是

Answer 1

cos(π/6-α)=根号3/3,
则cos(α-π/6)=根号3/3,
sin^2(α-π/6)=1- cos^2 (α-π/6)=2/3.

cos(5π/6+α)=cos[π-(π/6-α)]
=- cos(π/6-α)=-√3/3,

则sin^2(α-π/6)-cos(5π/6+α)
=2/3+√3/3.

Answer 2

原题应该是“已知cos(π/6-α)=根号3/3,则sin^2(α-π/6)-cos(5π/6+α)的值是” 吧
cos(5π/6+α) = cos(a - π/6 + π)=-cos(a - π/6)= -根号3/3;
sin^2(α-π/6)=1 - cos^2(π/6-α)=2/3
所以sin^2(α-π/6)-cos(5π/6+α)=2/3+根号3/3;