Question

How do you solve `2cos^2x+ cos x=1`?

Answer 1

As you may have noticed, this is a normal quadratic in `cos`.

Explanation:

`2cos^2x + 2cosx- cosx - 1 = 0`

`2cosx(cosx + 1) - (cosx + 1) = 0`

`(2cosx - 1)(cosx + 1) = 0`

`cosx = 1/2 and cosx = -1`

`x = 60^@, 300^@ and 180^@`

Hopefully this helps!