What is the value of cot(15°) – tan(15°) ?

Correct option is C

Given:

Expression: $$\cot(15^\circ) - \tan(15^\circ)$$​​

Concept Used:
Use trigonometric identity:

​$$\cot \theta = \frac{1}{\tan \theta}$$​​

Solution:

​​​​​$$\tan(15^\circ) = 2 - \sqrt{3}$$​​

So,

​$$\cot(15^\circ) = \frac{1}{2 - \sqrt{3}} = \frac{2 + \sqrt{3}}{(2 - \sqrt{3})(2 + \sqrt{3})} = \frac{2 + \sqrt{3}}{4 - 3} = 2 + \sqrt{3}$$​​

Now,

​$$\cot(15^\circ) - \tan(15^\circ) = (2 + \sqrt{3}) - (2 - \sqrt{3}) = 2\sqrt{3}$$​