若sin(α+π/12)=1/3,则cos(α+7π/12)的值为
问题描述：
若sin(α+π/12)=1/3,则cos(α+7π/12)的值为
答
把α+π/12看做整体为b,则sin b=1/3,所求为cos (b+π/2)=-sin b=-1/3
答
cos(α+7π/12)=cos(α+π/12+π/2)=-sin(α+π/12)=-1/3
答
cos(α+7π/12)
=cos(-α-7π/12)
=sin[π/2-(-α-7π/12)]
=sin(α+13π/12)
=sin[π+(α+π/12)]
=-sin(α+π/12)
=-1/3
答
cos(α+7π/12)
=cos(α+π/12)cos(π/2)-sin(α+π/12)sin(π/2)
=-sin(α+π/12)
=-1/3