Question

How do you find the general solutions for `2cosx - sqrt3 = 0`?

Answer 1

`x=2npi +-pi/6, AA n in ZZ`

Explanation:

`2cos(x)-sqrt(3)=0`

`rArrcolor(white)("XXX")cos(x) = sqrt(3)/2`

This is a standard trigonometric ratio for a `pi/6` reference angle.

Within the interval `(-pi,+pi]`
`color(white)("XXX")x = +pi/6 or x=-pi/6`

For all solutions it is necessary to include all possoble full circle increments:
`color(white)("XXX")x=2npi+-pi/6, AAn in ZZ`