You mention a double angle identity, so does that mean you wanted to find cos (10u)?
That's where would come in I guess; and yes, it does equal .
My function to integrate (don't know how to do integral symbol on here)
Use this double angle formula:
Rearranged:
Substitute values:
Evaluate:
Integrate:
Simplify:
You had the correct answer in the second last line of that other post. Nothing else you have written after it is correct. So that I am not repeating myself, I will say take much greater care with your basic algebra.
(I just do not understand how you can possibly propose this or the other final answer as being equivalent to that correct second last line)