Question

I need your opinion to improve the proof. Please

Answer 1

This is probably as simple as it can get. I don't see how you could improve it.

Now try prove this using the Chebyshev polynomial of the first kind which you just proved.
http://openstudy.com/study#/updates/55eda290e4b0819646d9d724

Answer 2

Well you could improve it by capturing a larger region and uploading it lol. Some parts of your prove are partially cut off.