若cos(a+pi/6)-sina=2sqrt(3)/3,则sin(a-7pi/6),简述过程

网友回答

cos(a+pi/6)-sina
=sin(π/2-a-π/6)-sina
=sin(2π/6-a)-sina
=sin(2π+2π/6-a)-sina
=sin(14π/6-a)-sina
=2sin(7π/6-a)cos(7π/6)
=-2cos(π/6)sin(7π/6-a)
=-√3sin(7π/6-a)
=√3sin(a-7π/6)
=2sqrt(3)/3
所以sin(a-7π/6)=2/3