Question

How do you solve `3cot2x-1=0`

Answer 1

Solve `3 cot (theta) - 1 = 0` for `theta`
then divide `theta` by `2`
(Sticking the `2x` in the `cot` function is a misleading trick).

`3 cot (theta) - 1 = 0`
`rarr cot (theta) = 1/3`
`rarr tan (theta) = 3`

Looking this up in standard tables, we get:
`theta = 1.249 radians`

So
`x = 0.6245 radians`