Factoring with the double angle formula for cosine

[Mechaman]

The Question:

My Attempt:

I use the 'Double Angle Formula' to get to the second line. Then multiply the sigma-x into what's in the brackets, then factor out at the end. I'm not sure how I reach the answer that's provided with the solution. Any help would be appreciated.

Thank You.

 

[FeDeX_LaTeX]

You've pretty much already got the answer. Just expand that last line and re-arrange.