How do I find a missing angle using a reciprocal trigonometric function?

Question

I just attempted this as best as I could, but I'm not sure if I'm correct.

Here's the work:

$$\cot x =\frac{1}{2}$$ $$\frac{1}{\tan{x}} = \frac{1}{\frac{1}{2}}$$ $$\frac{1}{\tan^{-1}\cdot\tan x} = \frac{1}{\tan^{-1}\cdot\frac{1}{2}}$$ $$\frac1x = \frac1{25.56505118}$$ $$x = 0.03911590057$$ Since I wasn't able to successfully search up anything relative to the matter, I'd appreciate if someone would tell me if this is correct. If not, then what are the correct steps that I'm supposed to take?

Answer 1

Here are the steps, \[ \cot x =\frac{1}{2} \] \[ \frac{1}{\tan x} =\frac{1}{2} \] \[ \tan x =2 \] \[ \arctan(\tan x)=\arctan 2 \] \[ x =\arctan 2=1.1071487\ \mbox{rad}= 63.43^{\circ} \]

Answer 2

I was unable to edit your question since there are places I cannot determine your intent. But you can proceed this way: $$\cot x = \frac{1}{2}$$ $$\frac{1}{{\tan x}} = \frac{1}{2}$$ $$\tan x = 2$$ Can you continue from there?