If cot A = $$\frac{1}{\sqrt3}$$​, then what is the value of ​$$\frac{\lparen1-cos\space2A\rparen}{\lparen1+cos\space2A\rparen}?$$​

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Correct option is D

Given:

​$$\cot A = \frac{1}{\sqrt{3}}$$​​

We need to determine the value of:

​$$\frac{1 - \cos 2A}{1 + \cos 2A}$$​​

Concept Used:

Using the identity:

​$$\cos 2A = \frac{1 - \tan^2 A}{1 + \tan^2 A}$$​​

​$$\frac{1 - \cos 2A}{1 + \cos 2A} = \tan^2A$$​

Solution:

​$$\tan A = \frac{1}{\cot A} = \sqrt{3}$$​​

​$$\tan^2 A = 3$$ 

So, 

​$$\frac{1 - \cos 2A}{1 + \cos 2A} = \tan^2 A =3$$​​

Thus, correct answer is option (D).