∵cosx=1-2sin²(x/2).∴cosx-1=-2sin²(x/2).又sinx=2sin(x/2)cos(x/2).∴原式=（sinx)/(cosx-1)=[2sin(x/2)cos(x/2)]/[-2sin²(x/2)]=-[cos(x/2)]/[sin(x/2)]=-cot(x/2).