if a cos theta equal to root 3 upon 2 at theta is acute then root 3 tan theta minus 10 cube theta is equal to

It seems like there's a bit of confusion in your question. However, I'll try to help as best as I can.

Given that cos(theta) = sqrt(3)/2, we can find sin(theta) using the Pythagorean identity sin^2(theta) + cos^2(theta) = 1. Solving for sin(theta) gives us sin(theta) = 1/2.

Now, tan(theta) = sin(theta)/cos(theta) = (1/2) / (sqrt(3)/2) = 1/sqrt(3).

Substituting this into the equation root(3) * tan(theta) - 10 * cube(theta), we get root(3) * (1/sqrt(3)) - 10 * cube(theta).

This simplifies to 1 - 10 * cube(theta).

Without additional information, we can't simplify this further. If there's a specific value for theta or if there's a typo in your question, please provide more details.