已知cos(x+π/12)=1/3,则sin(2x-π/3)的值为多少?

题目

已知cos(x+π/12)=1/3,则sin(2x-π/3)的值为多少?

答案

已知cos(x+π/12)=1/3,那么：
cos(2x+ π/6)=2cos²(x+π/12)-1=2/9 - 1=-7/9
所以：
sin(2x-π/3)=sin[(2x+ π/6)- π/2]
=-sin[π/2 -(2x+ π/6)]
=-cos(2x+ π/6)
=7/9