Find `sin``x/2``,cos``x/2` and `tan``x/2`of the following : `cotx=-1/3`, x in quadrant III

Explanation

To find \( \sin \frac{x}{2} \), \( \cos \frac{x}{2} \), and \( \tan \frac{x}{2} \) given that \( \cot x = -\frac{1}{3} \) and \( x \) is in the third quadrant, we can follow these steps:

### Step 1: Determine \( \tan x \)
Since \( \cot x = -\frac{1}{3} \), we can find \( \tan x \) as follows:
\[ \tan x = \frac{1}{\cot x} = \frac{1}{-\frac{1}{3}} = -3 \]

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