If sec theta = 2, find 4 cos theta-root 3 sin theta/tan theta

Cos theta = 1 / sec theta so cos theta = 1/2

and 4 cos theta = 4 * 1/2 = 2

sin theta = sqrt (1 - cos^2 theta) = sqrt 1 - 1/4) = sqrt (3/4) = sqrt3/2

root 3 sin theta = 3/2

tan theta = sin theta / cos theta = sqrt3 / 2 / 1/2 = 2*sqrt3 / 2 = sqrt3

so the answer is 2 - 3/2 / sqrt3 = 1/2 / sqrt3 = sqrt3 / 6