Question

How do you solve 2 cos x + 1 = cos x for all values of x on [0, 2pi]?

Answer 1

`cos x = -1 -> x = pi`

Explanation:

Subtract cos x from both sides:

So we have `1 cos x + 1 = 0`

Now, subtract 1 from both sides:

So we have `cos x = -1`

Draw the unit circle. When is `cos x` equal to negative one?

This happens when the angle is `pi` radians!

In the interval `[0, 2pi]` there is only one value for this, so `x = pi`