trigonometry: show that the arcosine (X) + arccos (y) = π / 2, Si and only if x = y

I was wondering about this identity:
arcosine (X) + arccos (X) = π / 2;
That a thought came to my mind that in general
arcsin (X) + arccos (Y) = π / 2, implied that X = Y.
I have a hunch that it's true and I've done a kind of self-test but it's illegal to use a test method, then I also tried to use graphics but I'm still stuck. I would be grateful if someone could help me please.

$ Π (x) ge log log x $ holds $ 2 le x e e {{e ^ 3} <5.3 times 10 ^ 8 $?

The book Theory of Numbers by G H Hardy, et al. test $ π (x) ge log log x $ for $ x> e ^ {e ^ 3} $. There is a way to try out that also goes for $ 2 le x e e ^ {e ^ 3} $ otherwise (in the worst case) some valuable source to verify this numerically?

calculation: How do I find x when θ = 1/4 π of dx / dθ = (x + 2) without ^ 2 2θ if x is 0 when θ is 0?

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