已知sin(π/6-x)=5/13,求cos(2π/3+2x)的值

题目

已知sin(π/6-x)=5/13,求cos(2π/3+2x)的值
高一数学!急!

答案

cos(2π/3+2x)
=-cos[π-(2π/3+2x)]
=-cos(π/3-2x)
=-cos[2(π/6-x)]
=-[1-2sin(π/6-x)^2] (利用倍角关系)
=-[1-2×(5/13)^2]
=-119/169