# What is the root x in equation square root 3 cos x - sin x = 0?

### 1 Answer | Add Yours

Supposing that you need to solve for x the equation `sqrt3*cos x - sin x = 0` , it is indicated to divide the equation both sides by `cos x` or by `sin x` .

Selecting the option to divide the equation by `cos x` yields:

`sqrt 3 - sin x/cos x = 0`

Using the trigonometric identity `sin x/cos x = tan x` yields:

`sqrt 3 - tan x = 0 => tan x = sqrt 3`

`x = tan^(-1)sqrt 3 + n*pi`

`x = pi/3 + n*pi`

**Hence, evaluating the general solution to the given equation, yields `x = pi/3 + n*pi` .**

**Sources:**