How do you solve -6[cot(2pi/3)-cot(pi/3)]?

Answer 1

You should have available to you :
- either in your notebook
-or in your text
- or memorized ,

the ratio of sides for the 30-60-90 as well as the 45-45-90 right-angled triangles

you should also have memorized the simple conversion from degrees to radians of the following
30° = π/6 radians
45° = π/4 radians
60° = π/3 radians
90° = π/2 radians
180° = π radians

so pulling apart your expression
cot(2π/3)
= 1/tan(120°)
but tan(120°) = -tan60° = -√3
cot(2π/3) = -1/√3

cot(π/3)
= 1/tan(60)
= 1/√3

-6[cot(2pi/3)-cot(pi/3)]
= -6[-1/√3 - 1/√3]
= -6(-2√3)
= 12/√3
= 12/√3 * √3/√3
= 12√3/3
= 4√3

btw, we did not "solve" the expression , we evaluated the expression. We solve equations, and there was no equation.