已知sin(α+π/12)＝1/3,求cos(α+7π/12)的值

题目

已知sin(α+π/12)＝1/3,求cos(α+7π/12)的值

答案

令x=α+π/12
则α=x-π/12
且sinx=1/3
所以原式=cos(x-π/12+7π/12)
=cos(x+π/2)
=*-sinx
=-1/3