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

Correct option is A

Given:

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

Solution:

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

cos x$$= (\sqrt{3} + 3)\sin x$$​​

$$\frac{\sin x}{\cos x} = \frac{1}{\sqrt{3} + 3}$$​​

​$$\tan x = \frac{1}{\sqrt{3} + 3} \times \frac{\sqrt{3} - 3}{\sqrt{3} - 3} = \frac{\sqrt{3} - 3}{(\sqrt{3})^2 - 9} = \frac{\sqrt{3} - 3}{3 - 9} = \frac{\sqrt{3} - 3}{-6}$$​​

​$$\tan x = \frac{3 - \sqrt{3}}{6}$$​