If cos x – 3sin x = $$\sqrt3$$​ sin x, then the value of tan x is:

Correct option is A

Given:

​$$\cos x - 3 \sin x = \sqrt{3} \sin x$$​

Formula Used:
tan x =$$\frac{\sin x}{\cos x}$$​​

Solution:

​$$\cos x = (\sqrt{3} + 3) \sin x \Rightarrow \frac{\sin x}{\cos x} = \frac{1}{\sqrt{3} + 3} \Rightarrow \tan x = \frac{1}{\sqrt{3} + 3}$$​​

​$$\tan x = \frac{1}{\sqrt{3} + 3} \cdot \frac{\sqrt{3} - 3}{\sqrt{3} - 3} = \frac{\sqrt{3} - 3}{(\sqrt{3} + 3)(\sqrt{3} - 3)} = \frac{\sqrt{3} - 3}{3 - 9} = \frac{\sqrt{3} - 3}{-6} = \frac{3 - \sqrt{3}}{6}$$​