若sin(π/6-α)=1/3,求cos(2π/3+2α)的值

题目

若sin(π/6-α)=1/3,求cos(2π/3+2α)的值

答案

sin(π/6-α)=cos(π/3+α)=1/3
cos(2π/3+2α)=2cos²(π/3+α)-1=2/9-1=-7/9