SOLUTION: Solve for x in the equation cos x - cos 2x = 1/2 where x e (0 degree, 180 degree)

Question 1199427: Solve for x in the equation cos x - cos 2x = 1/2 where x e (0 degree, 180 degree)
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Solve for x in the equation cos(x) - cos(2x) = 1/2
cos(2x) = 2cos^2(x) - 1
----
cos(x) - 2cos^2(x) + 1/2 = 0
2cos^2(x) - cos(x) - 1/2 = 0

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=5 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 0.809016994374947, -0.309016994374947. Here's your graph:

======================
cos(x) = 0.809016994374947
x = 36 degs
-----
cos(x) = -0.309016994374947
x = 108 degs
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