Problem: Cot theta -1/cot theta 1 =1-√3 /1 √3 , then find the acute angle theta.

Solution:

First, simplify the left side of the equation by finding a common denominator:
Cot theta -1/cot theta 1 = (cot^2 theta - 1) / cot theta
= (-csc^2 theta) / cot theta
= -cos theta / sin theta

Now, substitute this expression into the original equation and simplify:
-cos theta / sin theta - 1 = (1 - √3) / √3
Multiply both sides by √3 sin theta:
-√3 cos theta - sin theta = √3 - sin theta
Simplify:
-√3 cos theta = √3
cos theta = -1
theta = 180 degrees

However, since the problem asks for the acute angle theta, we need to find the equivalent acute angle within the first quadrant. Since cosine is negative in the second quadrant, we can find the equivalent acute angle by subtracting 180 degrees from 360 degrees:
theta = 360 degrees - 180 degrees = 180 degrees

Therefore, the acute angle theta is 180 degrees.

√3