Question

How do you solve `2cos^2 (x) = 3 cos (x)`?

Answer 1

If `cos(x) = 0` then `2cos^2(x) = 3 cos(x) = 0`, so that gives solutions of the form:

`x = pi/2 + n pi`, where `n` is any integer.

On the other hand, if `cos(x) != 0` then divide both sides of the equation by `2cos(x)` to get:

`cos x = 3/2`

Since `-1 <= cos x <= 1` for all values of `x`, this provides no more solutions.