若sin(π/6-x)=1/3,则cos(2π/3+2x)=___________

题目

若sin(π/6-x)=1/3,则cos(2π/3+2x)=___________

答案

cos(2π/3+2x)
=cos[π-(π/3-2x)]
=-cos(π/3-2x)
=-cos2(π/6-x)
=-[1-2sin²(π/6-x)]
=-[1-2*(1/3)²]
=-(1-2/9)
=-7/9