To simplify the expression TG(16π/3) - cos(-55π/6), we first need to find the exact values of the tangent and cosine of the given angles.

First, let's find the values of the tangent of 16π/3:
Tg(16π/3) = tan(16π/3) = tan(5π + π/3) = tan(π/3) = √3

Next, let's find the value of the cosine of -55π/6:
cos(-55π/6) = cos(-9π + π/6) = cos(-π/6) = cos(π/6) = √3/2

Now, we can substitute these values back into the original expression:
√3 - (√3/2) = √3 - √3/2 = (√3/2) - (√3/2) = 0

Therefore, TG(16π/3) - cos(-55π/6) simplifies to 0.