Question

Find all solutions of the equation 2cos3x=1 in the interval [0,π)

Answer 1

We first get cos(3x) by itself by dividing both sides by 2 to get
cos(3x) = 1/2

Now between 0 and pi, do you know where cosx is 1/2? Forget the 3x part for now, do you know where cosx = 1/2?

Answer 2

as @Psymon said \(\bf 2cos(3x)=1 \implies cos(3x) = \cfrac{1}{2}\\ \implies cos^{-1}(cos(3x)) = cos^{-1}\left(\cfrac{1}{2}\right)\\
3x = cos^{-1}\left(\cfrac{1}{2}\right)\)