Thanks for your help with the correction of my first attempt at the solution. I updated the page and hopefully it's better now.
I like how you use the Euler formula to illustrate the process of determining the system, however, I think a little more steps will make the final answer much easier to understand. - Bavorndej Chanyasak
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I do not believe your proof is correct. You state that
$ e^{2jt} = \cos{t} + 2 j\sin{t} $
I think that is false.
$ e^{2jt} = \cos{2t} + j \sin{2 t} $
This problem can be proven using Euler's formula but I think you have incorrectly applied it.
Also I encourage you to learn LaTeX. It makes mathmatical expressions much easier to read - Chris Cadwallader
