Originally Posted by

**dagbayani481** So the questions asks find all the values of x in interval [0,2pi)

for the following equation $\displaystyle 8 + 4 cos(2x) = 12 cos(x)$

So the way I go about solving it is I subtract 12cos(x) to the other side and replace cos(2x) for the double angle identity which gives me:

$\displaystyle 4 (2cos^2x-1) -12 cosx +8=0$

So essentially, I distribute the 4 and rewrite the equation as follows:

$\displaystyle 8cos^2x -12 cosx +4=0$

Next I take out the common factor of 4 and factor out the whole equation:

$\displaystyle 4 (2cos^2x -3 cosx + 1)=0$ to $\displaystyle (2cosx-1)(cosx-1)=0$

After solving each one I get the following answers: $\displaystyle x = \frac {\pi}{3}, \frac {5\pi}{3}, & 0$

However, the online assignment guide is telling me I've gotten the wrong answers. I'm honestly lost, can anyone tell me where exactly I'm getting this wrong?