Question

How do you find the general solutions for `1 - cos(x) = 1/2`?

Answer 1

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

Explanation:

If `1-cos(x) = 1/2`
then
`color(white)("XXXX")cos(x)=1/2`

This is one of the standard triangle ratios
with `x=pi/6` or `x=-pi/6`
`color(white)("XXXXXXXXXXXX")`if we restrict `x in [-pi,+pi]`

In general we can add any multiple of `2pi` to this result and gt what is effectively the same angles.