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Hi Omar,
My impression --- I didn't think about your post sufficiently closely to say with certainty --- is that one of the comments from either Raymond has answered the question you asked. I don't know if you still have access to the question now that it's been deleted, so I'll repost his comment:
For x=(2k+1)π/2 with k∈ℤ cos(x)=0 so that, in your second equation, you are evaluating 1/ζ(x0)=0 (because ζ becomes ∞ at 1). But cos(x)/2=0 at the right so that for these x your equality holds. Hoping this helped.
In any case, your question raised a few flags. You present a formula with no motivation, and only Wolfram Alpha as justification. Rather than asking a question in the title of your post, you say you've found an "amazing result". There are no question marks in your post, only a paranthetical reading:
(In case it is not clear I am asking if this, or its real part's relation to the cosine function, is correct. or if it is an error. )
Rather than editing your question, you post corrections in comments. Indeed, the question could easily have been closed based on Kevin's comment alone (that you asked for the imaginary part and apparently meant the real part). All of these contribute to your question looking like that of a crackpot.
So that's a possible answer to why your question was closed. Of course, I can't speak folks who did the actual closing, but it's my best guess. I'm not sure why it was locked and deleted, though.
In general, please keep in mind that MO is primarily for narrowly focused research questions. Importantly, it is not for announcing one's own results. Most importantly, at the end of the day your question was essentially precalculus-level. This is why it is inappropriate for MO.
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