Master Trigonometric Identities with Double Angle Techniques

[Mrencko]

I am doig trigonometric identities and i got this one, (all will be in the picture the solution and my work) i used the double angle for this but i am afraid i didn't get the exact idea, just guessing, good guessing, so i want to know how is the proper way to reach the solution

 

[SammyS]

Here is a little bigger view for folks.

So, I take it that you want to simplify $\ \sqrt{1+\cos(6\theta)\,}\$ using the double angle identity for cosine.

Write 6θ as 2(3θ) .