Question

Question #7142d

Answer 1

See below.

Explanation:

This is an identity:
`cos2x=2cos^2x-1`

Plugging it in:
`2(2cos^2-1)=cosx+1`

`4cos^2-2=cosx+1`

`4cos^2-cosx-3=0`

If we set `cosx=a`, then this is simply a quadratic, with two roots.

`4a^2-a-3=0`

`(4a+3)(a-1)=0`

`a=-3/4,1` or `cosx=-3/4,1`

These values all lie within the bounds of `cosx`, so we can calculate them periodically,

`cosx=1` when `x=0,2pi,4pi...2npi`, or `0,360,720,...360n`, where `n` is an integer.

`cosx=-3/4` is not as nice of a number.

`cos^-1(-3/4)=2.41885841` radians`+ 2nπ`, or `138.59037789° + 360°n`